---
_id: '31057'
abstract:
- lang: eng
text: In this paper we give an overview over some aspects of the modern mathematical
theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical
systems and their implications in physics. First we recall recent developments
in the mathematical theory of resonances, in particular how invariant Ruelle distributions
arise as residues of weighted zeta functions. Then we derive a correspondence
between weighted and semiclassical zeta functions in the setting of negatively
curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich
yields a high frequency interpretation of invariant Ruelle distributions as quantum
mechanical matrix coefficients in constant negative curvature. We finish by presenting
numerical calculations of phase space distributions in the more physical setting
of 3-disk scattering systems.
article_number: '244007'
article_type: review
author:
- first_name: Sonja
full_name: Barkhofen, Sonja
id: '48188'
last_name: Barkhofen
- first_name: Philipp
full_name: Schütte, Philipp
id: '50168'
last_name: Schütte
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
citation:
ama: 'Barkhofen S, Schütte P, Weich T. Semiclassical formulae For Wigner distributions.
Journal of Physics A: Mathematical and Theoretical. 2022;55(24). doi:10.1088/1751-8121/ac6d2b'
apa: 'Barkhofen, S., Schütte, P., & Weich, T. (2022). Semiclassical formulae
For Wigner distributions. Journal of Physics A: Mathematical and Theoretical,
55(24), Article 244007. https://doi.org/10.1088/1751-8121/ac6d2b'
bibtex: '@article{Barkhofen_Schütte_Weich_2022, title={Semiclassical formulae For
Wigner distributions}, volume={55}, DOI={10.1088/1751-8121/ac6d2b},
number={24244007}, journal={Journal of Physics A: Mathematical and Theoretical},
publisher={IOP Publishing Ltd}, author={Barkhofen, Sonja and Schütte, Philipp
and Weich, Tobias}, year={2022} }'
chicago: 'Barkhofen, Sonja, Philipp Schütte, and Tobias Weich. “Semiclassical Formulae
For Wigner Distributions.” Journal of Physics A: Mathematical and Theoretical
55, no. 24 (2022). https://doi.org/10.1088/1751-8121/ac6d2b.'
ieee: 'S. Barkhofen, P. Schütte, and T. Weich, “Semiclassical formulae For Wigner
distributions,” Journal of Physics A: Mathematical and Theoretical, vol.
55, no. 24, Art. no. 244007, 2022, doi: 10.1088/1751-8121/ac6d2b.'
mla: 'Barkhofen, Sonja, et al. “Semiclassical Formulae For Wigner Distributions.”
Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 24, 244007,
IOP Publishing Ltd, 2022, doi:10.1088/1751-8121/ac6d2b.'
short: 'S. Barkhofen, P. Schütte, T. Weich, Journal of Physics A: Mathematical and
Theoretical 55 (2022).'
date_created: 2022-05-04T12:23:11Z
date_updated: 2024-02-06T20:40:45Z
department:
- _id: '623'
- _id: '548'
- _id: '10'
doi: 10.1088/1751-8121/ac6d2b
external_id:
arxiv:
- '2201.04892'
intvolume: ' 55'
issue: '24'
language:
- iso: eng
publication: 'Journal of Physics A: Mathematical and Theoretical'
publisher: IOP Publishing Ltd
status: public
title: Semiclassical formulae For Wigner distributions
type: journal_article
user_id: '49178'
volume: 55
year: '2022'
...
---
_id: '31363'
abstract:
- lang: eng
text: Vorgestellt wird ein Entwicklungsforschungsprojekt zur Konzeption und Durchführung
einer Veranstaltung "Geometrie für Lehramtsstudierende". Die Schwerpunkte des
Projekts sind zum einen die inhaltliche Gestaltung der Veranstaltung und zum anderen
die Umsetzung von Professionsorientierung. Bezogen auf den inhaltlichen Aufbau
wird das auf metrischen Räumen aufbauende Axiomensystem der "Saccheri-Ebene" vorgestellt
und mit alternativen axiomatischen Zugängen zur ebenen Geometrie verglichen. Die
Frage nach der Umsetzung von Professionsorientierung in Fachveranstaltungen ist
eng mit der Problematik der zweiten Diskontinuität verbunden. In der Arbeit wird
dieses Problem auf Grundlage der Synthese von theoretischen Hintergründen zur
Bedeutung von mathematischem Wissen und Können für professionelle Handlungskompetenz
von Mathematiklehrkräften diskutiert und darauf aufbauend werden theoriebasierte
Entwurfsprinzipien für professionsorientierte Fachveranstaltungen entworfen. Zentrale
Elemente der methodischen Gestaltung sind die sogenannten "Schnittstellenwochen"
zu den Themen Kongruenz und Symmetrie sowie das begleitende Schnittstellen-ePortfolio.
Das zentrale Ergebnis der Arbeit ist ein theoretisch fundiertes und empirisch
evaluiertes ganzheitliches Veranstaltungskonzept für eine professionsorientierte
Geometrie-Veranstaltung für Lehramtsstudierende, dessen Konzeption auf andere
Fachveranstaltungen übertragbar ist. Darüber hinaus ergeben sich im Rahmen der
durchgeführten Entwicklungsforschung verschiedene neue Beiträge zur Geometriedidaktik
in Schule- und Hochschule.
- lang: eng
text: This thesis presents a design research project on the conception and implementation
of a course "Geometry for Student Teachers". The focal points of the project are,
on the one hand, the content structure of the course and, on the other hand, the
implementation of professional orientation. With regard to the content structure,
the axiom system of the "Saccheri plane", which is based on metric spaces, is
presented and compared with alternative axiomatic approaches to plane geometry.
The question of implementing professional orientation in mathematics courses is
closely connected to the problem of the second discontinuity. In the paper, this
problem is discussed on the basis of the synthesis of theoretical backgrounds
on the importance of mathematical knowledge and skills for professional competence
of mathematics teachers. Building on this, theory-based design principles for
profession-oriented subject courses are developed. Central elements of the methodological
design are the so-called "interface weeks" on the topics of congruence and symmetry
and an accompanying interface ePortfolio. The central result of the thesis is
a theoretically founded and empirically evaluated holistic course concept for
a profession-oriented geometry course for student teachers, the conception of
which is transferable to other subject events. In addition, various new contributions
to the didactics of geometry in schools and universities result from the desing
research.
author:
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
orcid: 0000-0002-6964-7123
citation:
ama: 'Hoffmann M. Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung
Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie
Für Lehramtsstudierende.; 2022. doi:10.17619/UNIPB/1-1313'
apa: 'Hoffmann, M. (2022). Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung
und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie
für Lehramtsstudierende. https://doi.org/10.17619/UNIPB/1-1313'
bibtex: '@book{Hoffmann_2022, title={Von der Axiomatik bis zur Schnittstellenaufgabe:
Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung
Geometrie für Lehramtsstudierende}, DOI={10.17619/UNIPB/1-1313},
author={Hoffmann, Max}, year={2022} }'
chicago: 'Hoffmann, Max. Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung
Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie
Für Lehramtsstudierende, 2022. https://doi.org/10.17619/UNIPB/1-1313.'
ieee: 'M. Hoffmann, Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung
und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie
für Lehramtsstudierende. 2022.'
mla: 'Hoffmann, Max. Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung
Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie
Für Lehramtsstudierende. 2022, doi:10.17619/UNIPB/1-1313.'
short: 'M. Hoffmann, Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung
Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie
Für Lehramtsstudierende, 2022.'
date_created: 2022-05-22T10:56:47Z
date_updated: 2024-02-19T06:28:58Z
department:
- _id: '97'
doi: 10.17619/UNIPB/1-1313
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://digital.ub.uni-paderborn.de/hs/content/titleinfo/6503170
oa: '1'
page: '410'
status: public
supervisor:
- first_name: Rolf
full_name: Biehler, Rolf
last_name: Biehler
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
title: 'Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung
eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende'
type: dissertation
user_id: '49063'
year: '2022'
...
---
_id: '35322'
author:
- first_name: Kai-Uwe
full_name: Bux, Kai-Uwe
last_name: Bux
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
citation:
ama: Bux K-U, Hilgert J, Weich T. Poisson transforms for trees of bounded degree.
Journal of Spectral Theory. 2022;12(2):659-681. doi:10.4171/jst/414
apa: Bux, K.-U., Hilgert, J., & Weich, T. (2022). Poisson transforms for trees
of bounded degree. Journal of Spectral Theory, 12(2), 659–681. https://doi.org/10.4171/jst/414
bibtex: '@article{Bux_Hilgert_Weich_2022, title={Poisson transforms for trees of
bounded degree}, volume={12}, DOI={10.4171/jst/414},
number={2}, journal={Journal of Spectral Theory}, publisher={European Mathematical
Society - EMS - Publishing House GmbH}, author={Bux, Kai-Uwe and Hilgert, Joachim
and Weich, Tobias}, year={2022}, pages={659–681} }'
chicago: 'Bux, Kai-Uwe, Joachim Hilgert, and Tobias Weich. “Poisson Transforms for
Trees of Bounded Degree.” Journal of Spectral Theory 12, no. 2 (2022):
659–81. https://doi.org/10.4171/jst/414.'
ieee: 'K.-U. Bux, J. Hilgert, and T. Weich, “Poisson transforms for trees of bounded
degree,” Journal of Spectral Theory, vol. 12, no. 2, pp. 659–681, 2022,
doi: 10.4171/jst/414.'
mla: Bux, Kai-Uwe, et al. “Poisson Transforms for Trees of Bounded Degree.” Journal
of Spectral Theory, vol. 12, no. 2, European Mathematical Society - EMS -
Publishing House GmbH, 2022, pp. 659–81, doi:10.4171/jst/414.
short: K.-U. Bux, J. Hilgert, T. Weich, Journal of Spectral Theory 12 (2022) 659–681.
date_created: 2023-01-06T08:49:06Z
date_updated: 2024-02-19T06:28:12Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
- _id: '91'
doi: 10.4171/jst/414
intvolume: ' 12'
issue: '2'
keyword:
- Geometry and Topology
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 659-681
publication: Journal of Spectral Theory
publication_identifier:
issn:
- 1664-039X
publication_status: published
publisher: European Mathematical Society - EMS - Publishing House GmbH
status: public
title: Poisson transforms for trees of bounded degree
type: journal_article
user_id: '49063'
volume: 12
year: '2022'
...
---
_id: '51554'
author:
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
citation:
ama: 'Hilgert J. Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second
Edition. AMS/MAA Press 2021. Mathematische Semesterberichte. 2022;69:151–153.
doi:10.1007/s00591-021-00314-7'
apa: 'Hilgert, J. (2022). Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics,
Second Edition. AMS/MAA Press 2021. In Mathematische Semesterberichte (Vol.
69, pp. 151–153). https://doi.org/10.1007/s00591-021-00314-7'
bibtex: '@article{Hilgert_2022, title={Ethan D. Bolker und Maura B. Mast: Common
Sense Mathematics, Second Edition. AMS/MAA Press 2021}, volume={69}, DOI={10.1007/s00591-021-00314-7},
journal={Mathematische Semesterberichte}, author={Hilgert, Joachim}, year={2022},
pages={151–153} }'
chicago: 'Hilgert, Joachim. “Ethan D. Bolker Und Maura B. Mast: Common Sense Mathematics,
Second Edition. AMS/MAA Press 2021.” Mathematische Semesterberichte, 2022.
https://doi.org/10.1007/s00591-021-00314-7.'
ieee: 'J. Hilgert, “Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics,
Second Edition. AMS/MAA Press 2021,” Mathematische Semesterberichte, vol.
69. pp. 151–153, 2022, doi: 10.1007/s00591-021-00314-7.'
mla: 'Hilgert, Joachim. “Ethan D. Bolker Und Maura B. Mast: Common Sense Mathematics,
Second Edition. AMS/MAA Press 2021.” Mathematische Semesterberichte, vol.
69, 2022, pp. 151–153, doi:10.1007/s00591-021-00314-7.'
short: J. Hilgert, Mathematische Semesterberichte 69 (2022) 151–153.
date_created: 2024-02-20T09:49:04Z
date_updated: 2024-02-20T09:52:53Z
department:
- _id: '91'
doi: 10.1007/s00591-021-00314-7
intvolume: ' 69'
language:
- iso: eng
page: 151–153
publication: Mathematische Semesterberichte
publication_status: published
status: public
title: 'Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition.
AMS/MAA Press 2021'
type: review
user_id: '49063'
volume: 69
year: '2022'
...
---
_id: '45970'
abstract:
- lang: eng
text: ' We introduce a new phase field model for tumor growth where viscoelastic
effects are taken into account. The model is derived from basic thermodynamical
principles and consists of a convected Cahn–Hilliard equation with source terms
for the tumor cells and a convected reaction–diffusion equation with boundary
supply for the nutrient. Chemotactic terms, which are essential for the invasive
behavior of tumors, are taken into account. The model is completed by a viscoelastic
system consisting of the Navier–Stokes equation for the hydrodynamic quantities,
and a general constitutive equation with stress relaxation for the left Cauchy–Green
tensor associated with the elastic part of the total mechanical response of the
viscoelastic material. For a specific choice of the elastic energy density and
with an additional dissipative term accounting for stress diffusion, we prove
existence of global-in-time weak solutions of the viscoelastic model for tumor
growth in two space dimensions [Formula: see text] by the passage to the limit
in a fully-discrete finite element scheme where a CFL condition, i.e. [Formula:
see text], is required. Moreover, in arbitrary dimensions [Formula:
see text], we show stability and existence of solutions for the fully-discrete
finite element scheme, where positive definiteness of the discrete Cauchy–Green
tensor is proved with a regularization technique that was first introduced by
Barrett and Boyaval [Existence and approximation of a (regularized) Oldroyd-B
model, Math. Models Methods Appl. Sci. 21 (2011) 1783–1837]. After that, we improve
the regularity results in arbitrary dimensions [Formula: see text] and in two
dimensions [Formula: see text], where a CFL condition is required. Then, in two
dimensions [Formula: see text], we pass to the limit in the discretization parameters
and show that subsequences of discrete solutions converge to a global-in-time
weak solution. Finally, we present numerical results in two dimensions [Formula:
see text]. '
author:
- first_name: Harald
full_name: Garcke, Harald
last_name: Garcke
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Dennis
full_name: Trautwein, Dennis
last_name: Trautwein
citation:
ama: Garcke H, Kovács B, Trautwein D. Viscoelastic Cahn–Hilliard models for tumor
growth. Mathematical Models and Methods in Applied Sciences. 2022;32(13):2673-2758.
doi:10.1142/s0218202522500634
apa: Garcke, H., Kovács, B., & Trautwein, D. (2022). Viscoelastic Cahn–Hilliard
models for tumor growth. Mathematical Models and Methods in Applied Sciences,
32(13), 2673–2758. https://doi.org/10.1142/s0218202522500634
bibtex: '@article{Garcke_Kovács_Trautwein_2022, title={Viscoelastic Cahn–Hilliard
models for tumor growth}, volume={32}, DOI={10.1142/s0218202522500634},
number={13}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World
Scientific Pub Co Pte Ltd}, author={Garcke, Harald and Kovács, Balázs and Trautwein,
Dennis}, year={2022}, pages={2673–2758} }'
chicago: 'Garcke, Harald, Balázs Kovács, and Dennis Trautwein. “Viscoelastic Cahn–Hilliard
Models for Tumor Growth.” Mathematical Models and Methods in Applied Sciences
32, no. 13 (2022): 2673–2758. https://doi.org/10.1142/s0218202522500634.'
ieee: 'H. Garcke, B. Kovács, and D. Trautwein, “Viscoelastic Cahn–Hilliard models
for tumor growth,” Mathematical Models and Methods in Applied Sciences,
vol. 32, no. 13, pp. 2673–2758, 2022, doi: 10.1142/s0218202522500634.'
mla: Garcke, Harald, et al. “Viscoelastic Cahn–Hilliard Models for Tumor Growth.”
Mathematical Models and Methods in Applied Sciences, vol. 32, no. 13, World
Scientific Pub Co Pte Ltd, 2022, pp. 2673–758, doi:10.1142/s0218202522500634.
short: H. Garcke, B. Kovács, D. Trautwein, Mathematical Models and Methods in Applied
Sciences 32 (2022) 2673–2758.
date_created: 2023-07-10T11:47:27Z
date_updated: 2024-04-03T09:15:35Z
department:
- _id: '841'
doi: 10.1142/s0218202522500634
intvolume: ' 32'
issue: '13'
keyword:
- Applied Mathematics
- Modeling and Simulation
language:
- iso: eng
page: 2673-2758
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
issn:
- 0218-2025
- 1793-6314
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: Viscoelastic Cahn–Hilliard models for tumor growth
type: journal_article
user_id: '100441'
volume: 32
year: '2022'
...
---
_id: '45969'
abstract:
- lang: eng
text: 'AbstractAn evolving surface finite element
discretisation is analysed for the evolution of a closed two-dimensional surface
governed by a system coupling a generalised forced mean curvature flow and a reaction–diffusion
process on the surface, inspired by a gradient flow of a coupled energy. Two algorithms
are proposed, both based on a system coupling the diffusion equation to evolution
equations for geometric quantities in the velocity law for the surface. One of
the numerical methods is proved to be convergent in the$$H^1$$H1norm
with optimal-order for finite elements of degree at least two. We present numerical
experiments illustrating the convergence behaviour and demonstrating the qualitative
properties of the flow: preservation of mean convexity, loss of convexity, weak
maximum principles, and the occurrence of self-intersections.'
author:
- first_name: Charles M.
full_name: Elliott, Charles M.
last_name: Elliott
- first_name: Harald
full_name: Garcke, Harald
last_name: Garcke
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Elliott CM, Garcke H, Kovács B. Numerical analysis for the interaction of mean
curvature flow and diffusion on closed surfaces. Numerische Mathematik.
2022;151(4):873-925. doi:10.1007/s00211-022-01301-3
apa: Elliott, C. M., Garcke, H., & Kovács, B. (2022). Numerical analysis for
the interaction of mean curvature flow and diffusion on closed surfaces. Numerische
Mathematik, 151(4), 873–925. https://doi.org/10.1007/s00211-022-01301-3
bibtex: '@article{Elliott_Garcke_Kovács_2022, title={Numerical analysis for the
interaction of mean curvature flow and diffusion on closed surfaces}, volume={151},
DOI={10.1007/s00211-022-01301-3},
number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business
Media LLC}, author={Elliott, Charles M. and Garcke, Harald and Kovács, Balázs},
year={2022}, pages={873–925} }'
chicago: 'Elliott, Charles M., Harald Garcke, and Balázs Kovács. “Numerical Analysis
for the Interaction of Mean Curvature Flow and Diffusion on Closed Surfaces.”
Numerische Mathematik 151, no. 4 (2022): 873–925. https://doi.org/10.1007/s00211-022-01301-3.'
ieee: 'C. M. Elliott, H. Garcke, and B. Kovács, “Numerical analysis for the interaction
of mean curvature flow and diffusion on closed surfaces,” Numerische Mathematik,
vol. 151, no. 4, pp. 873–925, 2022, doi: 10.1007/s00211-022-01301-3.'
mla: Elliott, Charles M., et al. “Numerical Analysis for the Interaction of Mean
Curvature Flow and Diffusion on Closed Surfaces.” Numerische Mathematik,
vol. 151, no. 4, Springer Science and Business Media LLC, 2022, pp. 873–925, doi:10.1007/s00211-022-01301-3.
short: C.M. Elliott, H. Garcke, B. Kovács, Numerische Mathematik 151 (2022) 873–925.
date_created: 2023-07-10T11:47:11Z
date_updated: 2024-04-03T09:15:44Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01301-3
intvolume: ' 151'
issue: '4'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 873-925
publication: Numerische Mathematik
publication_identifier:
issn:
- 0029-599X
- 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Numerical analysis for the interaction of mean curvature flow and diffusion
on closed surfaces
type: journal_article
user_id: '100441'
volume: 151
year: '2022'
...
---
_id: '45963'
abstract:
- lang: eng
text: AbstractThe scattering of electromagnetic
waves from obstacles with wave-material interaction in thin layers on the surface
is described by generalized impedance boundary conditions, which provide effective
approximate models. In particular, this includes a thin coating around a perfect
conductor and the skin effect of a highly conducting material. The approach taken
in this work is to derive, analyse and discretize a system of time-dependent boundary
integral equations that determines the tangential traces of the scattered electric
and magnetic fields. In a familiar second step, the fields are evaluated in the
exterior domain by a representation formula, which uses the time-dependent potential
operators of Maxwell’s equations. The time-dependent boundary integral equation
is discretized with Runge–Kutta based convolution quadrature in time and Raviart–Thomas
boundary elements in space. Using the frequency-explicit bounds from the well-posedness
analysis given here together with known approximation properties of the numerical
methods, the full discretization is proved to be stable and convergent, with explicitly
given rates in the case of sufficient regularity. Taking the same Runge–Kutta
based convolution quadrature for discretizing the time-dependent representation
formulas, the optimal order of convergence is obtained away from the scattering
boundary, whereas an order reduction occurs close to the boundary. The theoretical
results are illustrated by numerical experiments.
author:
- first_name: Jörg
full_name: Nick, Jörg
last_name: Nick
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Christian
full_name: Lubich, Christian
last_name: Lubich
citation:
ama: Nick J, Kovács B, Lubich C. Time-dependent electromagnetic scattering from
thin layers. Numerische Mathematik. 2022;150(4):1123-1164. doi:10.1007/s00211-022-01277-0
apa: Nick, J., Kovács, B., & Lubich, C. (2022). Time-dependent electromagnetic
scattering from thin layers. Numerische Mathematik, 150(4), 1123–1164.
https://doi.org/10.1007/s00211-022-01277-0
bibtex: '@article{Nick_Kovács_Lubich_2022, title={Time-dependent electromagnetic
scattering from thin layers}, volume={150}, DOI={10.1007/s00211-022-01277-0},
number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business
Media LLC}, author={Nick, Jörg and Kovács, Balázs and Lubich, Christian}, year={2022},
pages={1123–1164} }'
chicago: 'Nick, Jörg, Balázs Kovács, and Christian Lubich. “Time-Dependent Electromagnetic
Scattering from Thin Layers.” Numerische Mathematik 150, no. 4 (2022):
1123–64. https://doi.org/10.1007/s00211-022-01277-0.'
ieee: 'J. Nick, B. Kovács, and C. Lubich, “Time-dependent electromagnetic scattering
from thin layers,” Numerische Mathematik, vol. 150, no. 4, pp. 1123–1164,
2022, doi: 10.1007/s00211-022-01277-0.'
mla: Nick, Jörg, et al. “Time-Dependent Electromagnetic Scattering from Thin Layers.”
Numerische Mathematik, vol. 150, no. 4, Springer Science and Business Media
LLC, 2022, pp. 1123–64, doi:10.1007/s00211-022-01277-0.
short: J. Nick, B. Kovács, C. Lubich, Numerische Mathematik 150 (2022) 1123–1164.
date_created: 2023-07-10T11:44:57Z
date_updated: 2024-04-03T09:18:23Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01277-0
intvolume: ' 150'
issue: '4'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 1123-1164
publication: Numerische Mathematik
publication_identifier:
issn:
- 0029-599X
- 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Time-dependent electromagnetic scattering from thin layers
type: journal_article
user_id: '100441'
volume: 150
year: '2022'
...
---
_id: '45964'
abstract:
- lang: eng
text: "Abstract\r\n Maximal parabolic
$L^p$-regularity of linear parabolic equations on an evolving surface is shown
by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity
on a fixed surface. By freezing the coefficients in the parabolic equations at
a fixed time and utilizing a perturbation argument around the freezed time, it
is shown that backward difference time discretizations of linear parabolic equations
on an evolving surface along characteristic trajectories can preserve maximal
$L^p$-regularity in the discrete setting. The result is applied to prove the stability
and convergence of time discretizations of nonlinear parabolic equations on an
evolving surface, with linearly implicit backward differentiation formulae characteristic
trajectories of the surface, for general locally Lipschitz nonlinearities. The
discrete maximal $L^p$-regularity is used to prove the boundedness and stability
of numerical solutions in the $L^\\infty (0,T;W^{1,\\infty })$ norm, which is
used to bound the nonlinear terms in the stability analysis. Optimal-order error
estimates of time discretizations in the $L^\\infty (0,T;W^{1,\\infty })$ norm
is obtained by combining the stability analysis with the consistency estimates."
author:
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Buyang
full_name: Li, Buyang
last_name: Li
citation:
ama: Kovács B, Li B. Maximal regularity of backward difference time discretization
for evolving surface PDEs and its application to nonlinear problems. IMA Journal
of Numerical Analysis. Published online 2022. doi:10.1093/imanum/drac033
apa: Kovács, B., & Li, B. (2022). Maximal regularity of backward difference
time discretization for evolving surface PDEs and its application to nonlinear
problems. IMA Journal of Numerical Analysis. https://doi.org/10.1093/imanum/drac033
bibtex: '@article{Kovács_Li_2022, title={Maximal regularity of backward difference
time discretization for evolving surface PDEs and its application to nonlinear
problems}, DOI={10.1093/imanum/drac033},
journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
(OUP)}, author={Kovács, Balázs and Li, Buyang}, year={2022} }'
chicago: Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference
Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear
Problems.” IMA Journal of Numerical Analysis, 2022. https://doi.org/10.1093/imanum/drac033.
ieee: 'B. Kovács and B. Li, “Maximal regularity of backward difference time discretization
for evolving surface PDEs and its application to nonlinear problems,” IMA Journal
of Numerical Analysis, 2022, doi: 10.1093/imanum/drac033.'
mla: Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time
Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.”
IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2022,
doi:10.1093/imanum/drac033.
short: B. Kovács, B. Li, IMA Journal of Numerical Analysis (2022).
date_created: 2023-07-10T11:45:14Z
date_updated: 2024-04-03T09:17:59Z
department:
- _id: '841'
doi: 10.1093/imanum/drac033
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Maximal regularity of backward difference time discretization for evolving
surface PDEs and its application to nonlinear problems
type: journal_article
user_id: '100441'
year: '2022'
...
---
_id: '45966'
abstract:
- lang: eng
text: "Abstract\r\n This paper studies
bulk–surface splitting methods of first order for (semilinear) parabolic partial
differential equations with dynamic boundary conditions. The proposed Lie splitting
scheme is based on a reformulation of the problem as a coupled partial differential–algebraic
equation system, i.e., the boundary conditions are considered as a second dynamic
equation that is coupled to the bulk problem. The splitting approach is combined
with bulk–surface finite elements and an implicit Euler discretization of the
two subsystems. We prove first-order convergence of the resulting fully discrete
scheme in the presence of a weak CFL condition of the form $\\tau \\leqslant c
h$ for some constant $c>0$. The convergence is also illustrated numerically
using dynamic boundary conditions of Allen–Cahn type."
author:
- first_name: Robert
full_name: Altmann, Robert
last_name: Altmann
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Christoph
full_name: Zimmer, Christoph
last_name: Zimmer
citation:
ama: Altmann R, Kovács B, Zimmer C. Bulk–surface Lie splitting for parabolic problems
with dynamic boundary conditions. IMA Journal of Numerical Analysis. 2022;43(2):950-975.
doi:10.1093/imanum/drac002
apa: Altmann, R., Kovács, B., & Zimmer, C. (2022). Bulk–surface Lie splitting
for parabolic problems with dynamic boundary conditions. IMA Journal of Numerical
Analysis, 43(2), 950–975. https://doi.org/10.1093/imanum/drac002
bibtex: '@article{Altmann_Kovács_Zimmer_2022, title={Bulk–surface Lie splitting
for parabolic problems with dynamic boundary conditions}, volume={43}, DOI={10.1093/imanum/drac002}, number={2},
journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
(OUP)}, author={Altmann, Robert and Kovács, Balázs and Zimmer, Christoph}, year={2022},
pages={950–975} }'
chicago: 'Altmann, Robert, Balázs Kovács, and Christoph Zimmer. “Bulk–Surface Lie
Splitting for Parabolic Problems with Dynamic Boundary Conditions.” IMA Journal
of Numerical Analysis 43, no. 2 (2022): 950–75. https://doi.org/10.1093/imanum/drac002.'
ieee: 'R. Altmann, B. Kovács, and C. Zimmer, “Bulk–surface Lie splitting for parabolic
problems with dynamic boundary conditions,” IMA Journal of Numerical Analysis,
vol. 43, no. 2, pp. 950–975, 2022, doi: 10.1093/imanum/drac002.'
mla: Altmann, Robert, et al. “Bulk–Surface Lie Splitting for Parabolic Problems
with Dynamic Boundary Conditions.” IMA Journal of Numerical Analysis, vol.
43, no. 2, Oxford University Press (OUP), 2022, pp. 950–75, doi:10.1093/imanum/drac002.
short: R. Altmann, B. Kovács, C. Zimmer, IMA Journal of Numerical Analysis 43 (2022)
950–975.
date_created: 2023-07-10T11:45:49Z
date_updated: 2024-04-03T09:16:47Z
department:
- _id: '841'
doi: 10.1093/imanum/drac002
intvolume: ' 43'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 950-975
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions
type: journal_article
user_id: '100441'
volume: 43
year: '2022'
...
---
_id: '45968'
abstract:
- lang: eng
text: "Abstract\r\n We derive a numerical
method, based on operator splitting, to abstract parabolic semilinear boundary
coupled systems. The method decouples the linear components that describe the
coupling and the dynamics in the abstract bulk- and surface-spaces, and treats
the nonlinear terms similarly to an exponential integrator. The convergence proof
is based on estimates for a recursive formulation of the error, using the parabolic
smoothing property of analytic semigroups, and a careful comparison of the exact
and approximate flows. This analysis also requires a deep understanding of the
effects of the Dirichlet operator (the abstract version of the harmonic extension
operator), which is essential for the stable coupling in our method. Numerical
experiments, including problems with dynamic boundary conditions, reporting on
convergence rates are presented."
author:
- first_name: Petra
full_name: Csomós, Petra
last_name: Csomós
- first_name: Bálint
full_name: Farkas, Bálint
last_name: Farkas
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Csomós P, Farkas B, Kovács B. Error estimates for a splitting integrator for
abstract semilinear boundary coupled systems. IMA Journal of Numerical Analysis.
Published online 2022. doi:10.1093/imanum/drac079
apa: Csomós, P., Farkas, B., & Kovács, B. (2022). Error estimates for a splitting
integrator for abstract semilinear boundary coupled systems. IMA Journal of
Numerical Analysis. https://doi.org/10.1093/imanum/drac079
bibtex: '@article{Csomós_Farkas_Kovács_2022, title={Error estimates for a splitting
integrator for abstract semilinear boundary coupled systems}, DOI={10.1093/imanum/drac079},
journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
(OUP)}, author={Csomós, Petra and Farkas, Bálint and Kovács, Balázs}, year={2022}
}'
chicago: Csomós, Petra, Bálint Farkas, and Balázs Kovács. “Error Estimates for a
Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” IMA
Journal of Numerical Analysis, 2022. https://doi.org/10.1093/imanum/drac079.
ieee: 'P. Csomós, B. Farkas, and B. Kovács, “Error estimates for a splitting integrator
for abstract semilinear boundary coupled systems,” IMA Journal of Numerical
Analysis, 2022, doi: 10.1093/imanum/drac079.'
mla: Csomós, Petra, et al. “Error Estimates for a Splitting Integrator for Abstract
Semilinear Boundary Coupled Systems.” IMA Journal of Numerical Analysis,
Oxford University Press (OUP), 2022, doi:10.1093/imanum/drac079.
short: P. Csomós, B. Farkas, B. Kovács, IMA Journal of Numerical Analysis (2022).
date_created: 2023-07-10T11:46:54Z
date_updated: 2024-04-03T09:15:52Z
department:
- _id: '841'
doi: 10.1093/imanum/drac079
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Error estimates for a splitting integrator for abstract semilinear boundary
coupled systems
type: journal_article
user_id: '100441'
year: '2022'
...
---
_id: '45958'
abstract:
- lang: eng
text: AbstractIn this paper, we consider a non-linear
fourth-order evolution equation of Cahn–Hilliard-type on evolving surfaces with
prescribed velocity, where the non-linear terms are only assumed to have locally
Lipschitz derivatives. High-order evolving surface finite elements are used to
discretise the weak equation system in space, and a modified matrix–vector formulation
for the semi-discrete problem is derived. The anti-symmetric structure of the
equation system is preserved by the spatial discretisation. A new stability proof,
based on this structure, combined with consistency bounds proves optimal-order
and uniform-in-time error estimates. The paper is concluded by a variety of numerical
experiments.
author:
- first_name: Cedric Aaron
full_name: Beschle, Cedric Aaron
last_name: Beschle
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Beschle CA, Kovács B. Stability and error estimates for non-linear Cahn–Hilliard-type
equations on evolving surfaces. Numerische Mathematik. 2022;151(1):1-48.
doi:10.1007/s00211-022-01280-5
apa: Beschle, C. A., & Kovács, B. (2022). Stability and error estimates for
non-linear Cahn–Hilliard-type equations on evolving surfaces. Numerische Mathematik,
151(1), 1–48. https://doi.org/10.1007/s00211-022-01280-5
bibtex: '@article{Beschle_Kovács_2022, title={Stability and error estimates for
non-linear Cahn–Hilliard-type equations on evolving surfaces}, volume={151}, DOI={10.1007/s00211-022-01280-5},
number={1}, journal={Numerische Mathematik}, publisher={Springer Science and Business
Media LLC}, author={Beschle, Cedric Aaron and Kovács, Balázs}, year={2022}, pages={1–48}
}'
chicago: 'Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates
for Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” Numerische
Mathematik 151, no. 1 (2022): 1–48. https://doi.org/10.1007/s00211-022-01280-5.'
ieee: 'C. A. Beschle and B. Kovács, “Stability and error estimates for non-linear
Cahn–Hilliard-type equations on evolving surfaces,” Numerische Mathematik,
vol. 151, no. 1, pp. 1–48, 2022, doi: 10.1007/s00211-022-01280-5.'
mla: Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates for
Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” Numerische Mathematik,
vol. 151, no. 1, Springer Science and Business Media LLC, 2022, pp. 1–48, doi:10.1007/s00211-022-01280-5.
short: C.A. Beschle, B. Kovács, Numerische Mathematik 151 (2022) 1–48.
date_created: 2023-07-10T11:43:44Z
date_updated: 2024-04-03T09:19:34Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01280-5
intvolume: ' 151'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 1-48
publication: Numerische Mathematik
publication_identifier:
issn:
- 0029-599X
- 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Stability and error estimates for non-linear Cahn–Hilliard-type equations on
evolving surfaces
type: journal_article
user_id: '100441'
volume: 151
year: '2022'
...
---
_id: '45956'
abstract:
- lang: eng
text: "Abstract\r\n The full Maxwell
equations in the unbounded three-dimensional space coupled to the Landau–Lifshitz–Gilbert
equation serve as a well-tested model for ferromagnetic materials.\r\nWe propose
a weak formulation of the coupled system based on the boundary integral formulation
of the exterior Maxwell equations.\r\nWe show existence and partial uniqueness
of a weak solution and propose a new numerical algorithm based on finite elements
and boundary elements as spatial discretization with backward Euler and convolution
quadrature for the time domain.\r\nThis is the first numerical algorithm which
is able to deal with the coupled system of Landau–Lifshitz–Gilbert equation and
full Maxwell’s equations without any simplifications like quasi-static approximations
(e.g. eddy current model) and without restrictions on the shape of the domain
(e.g. convexity).\r\nWe show well-posedness and convergence of the numerical algorithm
under minimal assumptions on the regularity of the solution.\r\nThis is particularly
important as there are few regularity results available and one generally expects
the solution to be non-smooth.\r\nNumerical experiments illustrate and expand
on the theoretical results."
author:
- first_name: Jan
full_name: Bohn, Jan
last_name: Bohn
- first_name: Michael
full_name: Feischl, Michael
last_name: Feischl
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: 'Bohn J, Feischl M, Kovács B. FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
Equations via Convolution Quadrature: Weak Form and Numerical Approximation. Computational
Methods in Applied Mathematics. 2022;23(1):19-48. doi:10.1515/cmam-2022-0145'
apa: 'Bohn, J., Feischl, M., & Kovács, B. (2022). FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
Equations via Convolution Quadrature: Weak Form and Numerical Approximation. Computational
Methods in Applied Mathematics, 23(1), 19–48. https://doi.org/10.1515/cmam-2022-0145'
bibtex: '@article{Bohn_Feischl_Kovács_2022, title={FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
Equations via Convolution Quadrature: Weak Form and Numerical Approximation},
volume={23}, DOI={10.1515/cmam-2022-0145},
number={1}, journal={Computational Methods in Applied Mathematics}, publisher={Walter
de Gruyter GmbH}, author={Bohn, Jan and Feischl, Michael and Kovács, Balázs},
year={2022}, pages={19–48} }'
chicago: 'Bohn, Jan, Michael Feischl, and Balázs Kovács. “FEM-BEM Coupling for the
Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form
and Numerical Approximation.” Computational Methods in Applied Mathematics
23, no. 1 (2022): 19–48. https://doi.org/10.1515/cmam-2022-0145.'
ieee: 'J. Bohn, M. Feischl, and B. Kovács, “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
Equations via Convolution Quadrature: Weak Form and Numerical Approximation,”
Computational Methods in Applied Mathematics, vol. 23, no. 1, pp. 19–48,
2022, doi: 10.1515/cmam-2022-0145.'
mla: 'Bohn, Jan, et al. “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
Equations via Convolution Quadrature: Weak Form and Numerical Approximation.”
Computational Methods in Applied Mathematics, vol. 23, no. 1, Walter de
Gruyter GmbH, 2022, pp. 19–48, doi:10.1515/cmam-2022-0145.'
short: J. Bohn, M. Feischl, B. Kovács, Computational Methods in Applied Mathematics
23 (2022) 19–48.
date_created: 2023-07-10T11:43:13Z
date_updated: 2024-04-03T09:20:30Z
department:
- _id: '841'
doi: 10.1515/cmam-2022-0145
intvolume: ' 23'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- Numerical Analysis
language:
- iso: eng
page: 19-48
publication: Computational Methods in Applied Mathematics
publication_identifier:
issn:
- 1609-4840
- 1609-9389
publication_status: published
publisher: Walter de Gruyter GmbH
status: public
title: 'FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution
Quadrature: Weak Form and Numerical Approximation'
type: journal_article
user_id: '100441'
volume: 23
year: '2022'
...
---
_id: '52574'
author:
- first_name: Gerda
full_name: Werth, Gerda
id: '578'
last_name: Werth
citation:
ama: 'Werth G. Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde
Vaertings. In: Beiträge zum Mathematikunterricht. WTM; 2022. doi:https://doi.org/10.37626/GA9783959872089.0'
apa: Werth, G. (2022). Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde
Vaertings. Beiträge zum Mathematikunterricht. 56. Jahrestagung der Gesellschaft
für Didaktik der Mathematik, Frankfurt am. Main. https://doi.org/10.37626/GA9783959872089.0
bibtex: '@inproceedings{Werth_2022, place={Münster}, title={Neue Wege im mathematischen
Unterricht - Auf den Spuren Mathilde Vaertings}, DOI={https://doi.org/10.37626/GA9783959872089.0},
booktitle={Beiträge zum Mathematikunterricht}, publisher={WTM}, author={Werth,
Gerda}, year={2022} }'
chicago: 'Werth, Gerda. “Neue Wege im mathematischen Unterricht - Auf den Spuren
Mathilde Vaertings.” In Beiträge zum Mathematikunterricht. Münster: WTM,
2022. https://doi.org/10.37626/GA9783959872089.0.'
ieee: 'G. Werth, “Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde
Vaertings,” presented at the 56. Jahrestagung der Gesellschaft für Didaktik der
Mathematik, Frankfurt am. Main, 2022, doi: https://doi.org/10.37626/GA9783959872089.0.'
mla: Werth, Gerda. “Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde
Vaertings.” Beiträge zum Mathematikunterricht, WTM, 2022, doi:https://doi.org/10.37626/GA9783959872089.0.
short: 'G. Werth, in: Beiträge zum Mathematikunterricht, WTM, Münster, 2022.'
conference:
end_date: 2022-09-02
location: Frankfurt am. Main
name: 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik
start_date: 2022-08-29
date_created: 2024-03-14T11:17:56Z
date_updated: 2024-04-09T10:56:58Z
department:
- _id: '10'
- _id: '98'
- _id: '360'
doi: https://doi.org/10.37626/GA9783959872089.0
language:
- iso: ger
place: Münster
publication: Beiträge zum Mathematikunterricht
publication_status: published
publisher: WTM
status: public
title: Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings
type: conference
user_id: '578'
year: '2022'
...
---
_id: '53480'
author:
- first_name: Sara Naseem
full_name: Malik, Sara Naseem
id: '38640'
last_name: Malik
- first_name: Sebastian
full_name: Rezat, Sebastian
id: '31132'
last_name: Rezat
citation:
ama: 'Malik SN, Rezat S. Linguistic features of word problems that cause difficulties
for learners across the curriculum: A literature review. In: Proceedings on
the Twelfth Congress on the European Society for Research in Mathematics Education
(CERME 12). ERME / Free University of Bozen-Bolzano; 2022.'
apa: 'Malik, S. N., & Rezat, S. (2022). Linguistic features of word problems
that cause difficulties for learners across the curriculum: A literature review.
Proceedings on the Twelfth Congress on the European Society for Research in
Mathematics Education (CERME 12).'
bibtex: '@inproceedings{Malik_Rezat_2022, title={Linguistic features of word problems
that cause difficulties for learners across the curriculum: A literature review},
booktitle={Proceedings on the Twelfth Congress on the European Society for research
in Mathematics Education (CERME 12)}, publisher={ERME / Free University of Bozen-Bolzano},
author={Malik, Sara Naseem and Rezat, Sebastian}, year={2022} }'
chicago: 'Malik, Sara Naseem, and Sebastian Rezat. “Linguistic Features of Word
Problems That Cause Difficulties for Learners across the Curriculum: A Literature
Review.” In Proceedings on the Twelfth Congress on the European Society for
Research in Mathematics Education (CERME 12). ERME / Free University of Bozen-Bolzano,
2022.'
ieee: 'S. N. Malik and S. Rezat, “Linguistic features of word problems that cause
difficulties for learners across the curriculum: A literature review,” 2022.'
mla: 'Malik, Sara Naseem, and Sebastian Rezat. “Linguistic Features of Word Problems
That Cause Difficulties for Learners across the Curriculum: A Literature Review.”
Proceedings on the Twelfth Congress on the European Society for Research in
Mathematics Education (CERME 12), ERME / Free University of Bozen-Bolzano,
2022.'
short: 'S.N. Malik, S. Rezat, in: Proceedings on the Twelfth Congress on the European
Society for Research in Mathematics Education (CERME 12), ERME / Free University
of Bozen-Bolzano, 2022.'
date_created: 2024-04-14T12:12:49Z
date_updated: 2024-04-18T08:03:54Z
ddc:
- '370'
- '510'
department:
- _id: '360'
file:
- access_level: closed
content_type: application/pdf
creator: smalik
date_created: 2024-04-14T12:16:57Z
date_updated: 2024-04-14T12:16:57Z
file_id: '53481'
file_name: Malik_TWG09.pdf
file_size: 390439
relation: main_file
success: 1
file_date_updated: 2024-04-14T12:16:57Z
has_accepted_license: '1'
language:
- iso: eng
publication: Proceedings on the Twelfth Congress on the European Society for research
in Mathematics Education (CERME 12)
publisher: ERME / Free University of Bozen-Bolzano
status: public
title: 'Linguistic features of word problems that cause difficulties for learners
across the curriculum: A literature review'
type: conference
user_id: '31132'
year: '2022'
...
---
_id: '44689'
abstract:
- lang: eng
text: AbstractEven in the digital age, learning
mathematics at an academic level still requires much reading of mathematical text.
Research has shown that reading mathematical text requires readers to engage with
all the structures of the book and with its pedagogical voice, making connections,
and plausible reasoning. Specific practices and strategies that support the close
reading of mathematical text have been suggested; however, descriptions and empirical
evaluations of materials designed to support these activities are rare. We present
the design and first evaluation cycle of materials developed in a design research
project that aims to scaffold close reading of mathematical text. The materials
were designed and evaluated in a German university course on elementary geometry
for first-year teacher education students who study mathematics to become primary
teachers. The reading strategies were explained and modeled for students in reading-strategy
videos. Additionally, close reading of mathematical text was scaffolded by close-reading
tasks and homework tasks and problems that build on the reading strategies and
were specifically designed to foster understanding of the mathematical text. Survey
data were collected from 296 students to evaluate their use of and attitude toward
the different materials. The quantitative results indicate that students used
the materials and were generally able to learn the course content by themselves.
From all provided materials, they found the close-reading tasks most helpful.
A qualitative analysis of answers to open questions revealed issues with different
materials, particularly with the script, and requests for additional materials.
The issues with the script were categorized inductively. The categories are presented
as a qualitative result of the study and discussed.
author:
- first_name: Sebastian
full_name: Rezat, Sebastian
id: '31132'
last_name: Rezat
- first_name: Sara Naseem
full_name: Malik, Sara Naseem
id: '38640'
last_name: Malik
- first_name: Markus
full_name: Leifeld, Markus
last_name: Leifeld
citation:
ama: 'Rezat S, Malik SN, Leifeld M. Scaffolding Close Reading of Mathematical Text
in Pre-service Primary Teacher Education at the Tertiary Level: Design and Evaluation.
International Journal of Science and Mathematics Education. 2022;20(S1):215-236.
doi:10.1007/s10763-022-10309-y'
apa: 'Rezat, S., Malik, S. N., & Leifeld, M. (2022). Scaffolding Close Reading
of Mathematical Text in Pre-service Primary Teacher Education at the Tertiary
Level: Design and Evaluation. International Journal of Science and Mathematics
Education, 20(S1), 215–236. https://doi.org/10.1007/s10763-022-10309-y'
bibtex: '@article{Rezat_Malik_Leifeld_2022, title={Scaffolding Close Reading of
Mathematical Text in Pre-service Primary Teacher Education at the Tertiary Level:
Design and Evaluation}, volume={20}, DOI={10.1007/s10763-022-10309-y},
number={S1}, journal={International Journal of Science and Mathematics Education},
publisher={Springer}, author={Rezat, Sebastian and Malik, Sara Naseem and Leifeld,
Markus}, year={2022}, pages={215–236} }'
chicago: 'Rezat, Sebastian, Sara Naseem Malik, and Markus Leifeld. “Scaffolding
Close Reading of Mathematical Text in Pre-Service Primary Teacher Education at
the Tertiary Level: Design and Evaluation.” International Journal of Science
and Mathematics Education 20, no. S1 (2022): 215–36. https://doi.org/10.1007/s10763-022-10309-y.'
ieee: 'S. Rezat, S. N. Malik, and M. Leifeld, “Scaffolding Close Reading of Mathematical
Text in Pre-service Primary Teacher Education at the Tertiary Level: Design and
Evaluation,” International Journal of Science and Mathematics Education,
vol. 20, no. S1, pp. 215–236, 2022, doi: 10.1007/s10763-022-10309-y.'
mla: 'Rezat, Sebastian, et al. “Scaffolding Close Reading of Mathematical Text in
Pre-Service Primary Teacher Education at the Tertiary Level: Design and Evaluation.”
International Journal of Science and Mathematics Education, vol. 20, no.
S1, Springer, 2022, pp. 215–36, doi:10.1007/s10763-022-10309-y.'
short: S. Rezat, S.N. Malik, M. Leifeld, International Journal of Science and Mathematics
Education 20 (2022) 215–236.
date_created: 2023-05-09T14:03:15Z
date_updated: 2024-04-18T08:22:47Z
department:
- _id: '360'
doi: 10.1007/s10763-022-10309-y
intvolume: ' 20'
issue: S1
keyword:
- General Mathematics
- Education
language:
- iso: eng
page: 215-236
publication: International Journal of Science and Mathematics Education
publication_identifier:
issn:
- 1571-0068
- 1573-1774
publication_status: published
publisher: Springer
quality_controlled: '1'
status: public
title: 'Scaffolding Close Reading of Mathematical Text in Pre-service Primary Teacher
Education at the Tertiary Level: Design and Evaluation'
type: journal_article
user_id: '31132'
volume: 20
year: '2022'
...
---
_id: '48389'
author:
- first_name: Jennifer
full_name: Dröse, Jennifer
id: '85820'
last_name: Dröse
- first_name: Birgit
full_name: Griese, Birgit
last_name: Griese
- first_name: Lena
full_name: Wessel, Lena
id: '85190'
last_name: Wessel
citation:
ama: 'Dröse J, Griese B, Wessel L. Prospective teachers’ diagnostic judgments on
students’ understanding of conditional probabilities. In: Twelfth Congress
of the European Society for Research in Mathematics Education (CERME12). ;
2022.'
apa: Dröse, J., Griese, B., & Wessel, L. (2022). Prospective teachers’ diagnostic
judgments on students’ understanding of conditional probabilities. Twelfth
Congress of the European Society for Research in Mathematics Education (CERME12).
TwelfthCongressoftheEuropeanSocietyforResearchin Mathematics Education(CERME12),
Bozen-Bolzano,Italy.
bibtex: '@inproceedings{Dröse_Griese_Wessel_2022, title={Prospective teachers’ diagnostic
judgments on students’ understanding of conditional probabilities}, booktitle={Twelfth
Congress of the European Society for Research in Mathematics Education (CERME12)},
author={Dröse, Jennifer and Griese, Birgit and Wessel, Lena}, year={2022} }'
chicago: Dröse, Jennifer, Birgit Griese, and Lena Wessel. “Prospective Teachers’
Diagnostic Judgments on Students’ Understanding of Conditional Probabilities.”
In Twelfth Congress of the European Society for Research in Mathematics Education
(CERME12), 2022.
ieee: J. Dröse, B. Griese, and L. Wessel, “Prospective teachers’ diagnostic judgments
on students’ understanding of conditional probabilities,” presented at the TwelfthCongressoftheEuropeanSocietyforResearchin
Mathematics Education(CERME12), Bozen-Bolzano,Italy, 2022.
mla: Dröse, Jennifer, et al. “Prospective Teachers’ Diagnostic Judgments on Students’
Understanding of Conditional Probabilities.” Twelfth Congress of the European
Society for Research in Mathematics Education (CERME12), 2022.
short: 'J. Dröse, B. Griese, L. Wessel, in: Twelfth Congress of the European Society
for Research in Mathematics Education (CERME12), 2022.'
conference:
location: Bozen-Bolzano,Italy
name: TwelfthCongressoftheEuropeanSocietyforResearchin Mathematics Education(CERME12)
start_date: Feb2022
date_created: 2023-10-23T10:56:02Z
date_updated: 2024-04-18T08:59:49Z
department:
- _id: '643'
language:
- iso: eng
main_file_link:
- url: https://hal.science/hal-03744585/
publication: Twelfth Congress of the European Society for Research in Mathematics
Education (CERME12)
quality_controlled: '1'
status: public
title: Prospective teachers’ diagnostic judgments on students’ understanding of conditional
probabilities
type: conference
user_id: '37888'
year: '2022'
...
---
_id: '48325'
author:
- first_name: Anna
full_name: Dellori, Anna
id: '57818'
last_name: Dellori
- first_name: Lena
full_name: Wessel, Lena
id: '85190'
last_name: Wessel
citation:
ama: Dellori A, Wessel L. Entwicklung und Erprobung von professionsorientierten
Lernumgebungen zur Wissensvernetzung in der Algebra. Beiträge zum Mathematikunterricht
2022. Published online 2022:665-668. doi:10.17877/DE290R-23598
apa: Dellori, A., & Wessel, L. (2022). Entwicklung und Erprobung von professionsorientierten
Lernumgebungen zur Wissensvernetzung in der Algebra. Beiträge zum Mathematikunterricht
2022, 665–668. https://doi.org/10.17877/DE290R-23598
bibtex: '@article{Dellori_Wessel_2022, title={Entwicklung und Erprobung von professionsorientierten
Lernumgebungen zur Wissensvernetzung in der Algebra}, DOI={10.17877/DE290R-23598},
journal={Beiträge zum Mathematikunterricht 2022}, publisher={LibreCat University},
author={Dellori, Anna and Wessel, Lena}, year={2022}, pages={665–668} }'
chicago: Dellori, Anna, and Lena Wessel. “Entwicklung und Erprobung von professionsorientierten
Lernumgebungen zur Wissensvernetzung in der Algebra.” Beiträge zum Mathematikunterricht
2022, 2022, 665–68. https://doi.org/10.17877/DE290R-23598.
ieee: 'A. Dellori and L. Wessel, “Entwicklung und Erprobung von professionsorientierten
Lernumgebungen zur Wissensvernetzung in der Algebra,” Beiträge zum Mathematikunterricht
2022, pp. 665–668, 2022, doi: 10.17877/DE290R-23598.'
mla: Dellori, Anna, and Lena Wessel. “Entwicklung und Erprobung von professionsorientierten
Lernumgebungen zur Wissensvernetzung in der Algebra.” Beiträge zum Mathematikunterricht
2022, LibreCat University, 2022, pp. 665–68, doi:10.17877/DE290R-23598.
short: A. Dellori, L. Wessel, Beiträge zum Mathematikunterricht 2022 (2022) 665–668.
date_created: 2023-10-19T09:37:24Z
date_updated: 2024-04-18T09:14:52Z
department:
- _id: '643'
doi: 10.17877/DE290R-23598
language:
- iso: ger
main_file_link:
- url: http://dx.doi.org/10.17877/DE290R-23598
page: 665-668
publication: Beiträge zum Mathematikunterricht 2022
publisher: LibreCat University
status: public
title: Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung
in der Algebra
type: journal_article
user_id: '37888'
year: '2022'
...
---
_id: '48385'
author:
- first_name: Anna
full_name: Dellori, Anna
id: '57818'
last_name: Dellori
- first_name: Lena
full_name: Wessel, Lena
id: '85190'
last_name: Wessel
citation:
ama: 'Dellori A, Wessel L. Design principles for intertwining local and nonlocal
mathematics - The case of relating registers and representations in abstract algebra.
In: Trigueros M, Barquero B, Hochmuth R, Peters J, eds. Proceedings of INDRUM2022.
; 2022:572-573.'
apa: Dellori, A., & Wessel, L. (2022). Design principles for intertwining local
and nonlocal mathematics - The case of relating registers and representations
in abstract algebra. In M. Trigueros, B. Barquero, R. Hochmuth, & J. Peters
(Eds.), Proceedings of INDRUM2022 (pp. 572–573).
bibtex: '@inbook{Dellori_Wessel_2022, title={Design principles for intertwining
local and nonlocal mathematics - The case of relating registers and representations
in abstract algebra}, booktitle={Proceedings of INDRUM2022}, author={Dellori,
Anna and Wessel, Lena}, editor={Trigueros, M. and Barquero, B. and Hochmuth, R.
and Peters, J.}, year={2022}, pages={572–573} }'
chicago: Dellori, Anna, and Lena Wessel. “Design Principles for Intertwining Local
and Nonlocal Mathematics - The Case of Relating Registers and Representations
in Abstract Algebra.” In Proceedings of INDRUM2022, edited by M. Trigueros,
B. Barquero, R. Hochmuth, and J. Peters, 572–73, 2022.
ieee: A. Dellori and L. Wessel, “Design principles for intertwining local and nonlocal
mathematics - The case of relating registers and representations in abstract algebra,”
in Proceedings of INDRUM2022, M. Trigueros, B. Barquero, R. Hochmuth, and
J. Peters, Eds. 2022, pp. 572–573.
mla: Dellori, Anna, and Lena Wessel. “Design Principles for Intertwining Local and
Nonlocal Mathematics - The Case of Relating Registers and Representations in Abstract
Algebra.” Proceedings of INDRUM2022, edited by M. Trigueros et al., 2022,
pp. 572–73.
short: 'A. Dellori, L. Wessel, in: M. Trigueros, B. Barquero, R. Hochmuth, J. Peters
(Eds.), Proceedings of INDRUM2022, 2022, pp. 572–573.'
date_created: 2023-10-23T09:40:30Z
date_updated: 2024-04-18T09:16:53Z
department:
- _id: '643'
editor:
- first_name: M.
full_name: Trigueros, M.
last_name: Trigueros
- first_name: B.
full_name: Barquero, B.
last_name: Barquero
- first_name: R.
full_name: Hochmuth, R.
last_name: Hochmuth
- first_name: J.
full_name: Peters, J.
last_name: Peters
language:
- iso: eng
page: 572-573
publication: Proceedings of INDRUM2022
status: public
title: Design principles for intertwining local and nonlocal mathematics - The case
of relating registers and representations in abstract algebra
type: book_chapter
user_id: '37888'
year: '2022'
...
---
_id: '48407'
author:
- first_name: Anna
full_name: Dellori, Anna
id: '57818'
last_name: Dellori
- first_name: Lena
full_name: Wessel, Lena
id: '85190'
last_name: Wessel
citation:
ama: 'Dellori A, Wessel L. Pre-service Teachers’ Professional Development: Relating
Abstract Algebra and School Algebra. In: Karunakaran SS, Higgins A, eds. Proceedings
of the 24th Annual Conference on Research in Undergraduate Mathematics Education.
MA; 2022:1177.'
apa: 'Dellori, A., & Wessel, L. (2022). Pre-service Teachers’ Professional Development:
Relating Abstract Algebra and School Algebra. In S. S. Karunakaran & A. Higgins
(Eds.), Proceedings of the 24th Annual Conference on Research in Undergraduate
Mathematics Education (p. 1177). MA.'
bibtex: '@inbook{Dellori_Wessel_2022, place={Boston}, title={Pre-service Teachers’
Professional Development: Relating Abstract Algebra and School Algebra}, booktitle={Proceedings
of the 24th Annual Conference on Research in Undergraduate Mathematics Education},
publisher={MA}, author={Dellori, Anna and Wessel, Lena}, editor={Karunakaran,
S.S. and Higgins, A.}, year={2022}, pages={1177} }'
chicago: 'Dellori, Anna, and Lena Wessel. “Pre-Service Teachers’ Professional Development:
Relating Abstract Algebra and School Algebra.” In Proceedings of the 24th Annual
Conference on Research in Undergraduate Mathematics Education, edited by S.S.
Karunakaran and A. Higgins, 1177. Boston: MA, 2022.'
ieee: 'A. Dellori and L. Wessel, “Pre-service Teachers’ Professional Development:
Relating Abstract Algebra and School Algebra,” in Proceedings of the 24th Annual
Conference on Research in Undergraduate Mathematics Education, S. S. Karunakaran
and A. Higgins, Eds. Boston: MA, 2022, p. 1177.'
mla: 'Dellori, Anna, and Lena Wessel. “Pre-Service Teachers’ Professional Development:
Relating Abstract Algebra and School Algebra.” Proceedings of the 24th Annual
Conference on Research in Undergraduate Mathematics Education, edited by S.S.
Karunakaran and A. Higgins, MA, 2022, p. 1177.'
short: 'A. Dellori, L. Wessel, in: S.S. Karunakaran, A. Higgins (Eds.), Proceedings
of the 24th Annual Conference on Research in Undergraduate Mathematics Education,
MA, Boston, 2022, p. 1177.'
date_created: 2023-10-24T07:28:19Z
date_updated: 2024-04-18T09:18:08Z
department:
- _id: '643'
editor:
- first_name: S.S.
full_name: Karunakaran, S.S.
last_name: Karunakaran
- first_name: A.
full_name: Higgins, A.
last_name: Higgins
language:
- iso: eng
page: '1177'
place: Boston
publication: Proceedings of the 24th Annual Conference on Research in Undergraduate
Mathematics Education
publisher: MA
status: public
title: 'Pre-service Teachers'' Professional Development: Relating Abstract Algebra
and School Algebra'
type: book_chapter
user_id: '37888'
year: '2022'
...
---
_id: '48408'
author:
- first_name: Lena
full_name: Wessel, Lena
id: '85190'
last_name: Wessel
- first_name: Jennifer
full_name: Dröse, Jennifer
id: '85820'
last_name: Dröse
citation:
ama: 'Wessel L, Dröse J. Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv
gestalten. mathematik lehren. 2022;233:33-36.'
apa: 'Wessel, L., & Dröse, J. (2022). Schreiben will gelernt sein: Schreiblerngelegenheiten
adaptiv gestalten. mathematik lehren, 233, 33–36.'
bibtex: '@article{Wessel_Dröse_2022, title={Schreiben will gelernt sein: Schreiblerngelegenheiten
adaptiv gestalten}, volume={233}, journal={mathematik lehren}, author={Wessel,
Lena and Dröse, Jennifer}, year={2022}, pages={33–36} }'
chicago: 'Wessel, Lena, and Jennifer Dröse. “Schreiben will gelernt sein: Schreiblerngelegenheiten
adaptiv gestalten.” mathematik lehren 233 (2022): 33–36.'
ieee: 'L. Wessel and J. Dröse, “Schreiben will gelernt sein: Schreiblerngelegenheiten
adaptiv gestalten,” mathematik lehren, vol. 233, pp. 33–36, 2022.'
mla: 'Wessel, Lena, and Jennifer Dröse. “Schreiben will gelernt sein: Schreiblerngelegenheiten
adaptiv gestalten.” mathematik lehren, vol. 233, 2022, pp. 33–36.'
short: L. Wessel, J. Dröse, mathematik lehren 233 (2022) 33–36.
date_created: 2023-10-24T07:33:17Z
date_updated: 2024-04-18T09:18:16Z
department:
- _id: '643'
intvolume: ' 233'
language:
- iso: ger
page: 33-36
publication: mathematik lehren
status: public
title: 'Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten'
type: journal_article
user_id: '37888'
volume: 233
year: '2022'
...