@article{44468,
  author       = {{Schmidt, Stephan and Gräßer, Melanie and Schmid, Hans-Joachim}},
  issn         = {{1064-8275}},
  journal      = {{SIAM Journal on Scientific Computing}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{4}},
  pages        = {{B1175--B1194}},
  publisher    = {{Society for Industrial & Applied Mathematics (SIAM)}},
  title        = {{{A Shape Newton Scheme for Deforming Shells with Application to Capillary Bridges}}},
  doi          = {{10.1137/20m1389054}},
  volume       = {{44}},
  year         = {{2022}},
}

@article{33657,
  author       = {{Mirhosseini, Hossein and Tahmasbi, Hossein and Kuchana, Sai Ram and Ghasemi, Alireza and Kühne, Thomas}},
  issn         = {{0927-0256}},
  journal      = {{Computational Materials Science}},
  keywords     = {{Computational Mathematics, General Physics and Astronomy, Mechanics of Materials, General Materials Science, General Chemistry, General Computer Science}},
  publisher    = {{Elsevier BV}},
  title        = {{{An automated approach for developing neural network interatomic potentials with FLAME}}},
  doi          = {{10.1016/j.commatsci.2021.110567}},
  volume       = {{197}},
  year         = {{2021}},
}

@article{45962,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow and powers of mean and inverse mean curvature flow. Error estimates are proved for semidiscretizations and full discretizations for the generalized flow. The algorithm proposed and studied here combines evolving surface finite elements, whose nodes determine the discrete surface, and linearly implicit backward difference formulae for time integration. The numerical method is based on a system coupling the surface evolution to nonlinear second-order parabolic evolution equations for the normal velocity and normal vector. A convergence proof is presented in the case of finite elements of polynomial degree at least 2 and backward difference formulae of orders 2 to 5. The error analysis combines stability estimates and consistency estimates to yield optimal-order $H^1$-norm error bounds for the computed surface position, velocity, normal vector, normal velocity and therefore for the mean curvature. The stability analysis is performed in the matrix–vector formulation and is independent of geometric arguments, which only enter the consistency analysis. Numerical experiments are presented to illustrate the convergence results and also to report on monotone quantities, e.g. Hawking mass for inverse mean curvature flow, and complemented by experiments for nonconvex surfaces.</jats:p>}},
  author       = {{Binz, Tim and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{3}},
  pages        = {{2545--2588}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{A convergent finite element algorithm for generalized mean curvature flows of closed surfaces}}},
  doi          = {{10.1093/imanum/drab043}},
  volume       = {{42}},
  year         = {{2021}},
}

@article{45957,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>A proof of convergence is given for a bulk–surface finite element semidiscretisation of the Cahn–Hilliard equation with Cahn–Hilliard-type dynamic boundary conditions in a smooth domain. The semidiscretisation is studied in an abstract weak formulation as a second-order system. Optimal-order uniform-in-time error estimates are shown in the $L^2$- and $H^1$-norms. The error estimates are based on a consistency and stability analysis. The proof of stability is performed in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second-order system. Numerical experiments illustrate the theoretical results.</jats:p>}},
  author       = {{Harder, Paula and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{3}},
  pages        = {{2589--2620}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions}}},
  doi          = {{10.1093/imanum/drab045}},
  volume       = {{42}},
  year         = {{2021}},
}

@article{45961,
  author       = {{Nick, Jörg and Kovács, Balázs and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{4}},
  pages        = {{997--1000}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations}}},
  doi          = {{10.1007/s00211-021-01196-6}},
  volume       = {{147}},
  year         = {{2021}},
}

@article{45959,
  author       = {{Kovács, Balázs and Li, Buyang and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{3}},
  pages        = {{595--643}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A convergent evolving finite element algorithm for Willmore flow of closed surfaces}}},
  doi          = {{10.1007/s00211-021-01238-z}},
  volume       = {{149}},
  year         = {{2021}},
}

@article{34629,
  author       = {{Hesse, Kerstin and Sloan, Ian H. and Womersley, Robert S.}},
  issn         = {{0377-0427}},
  journal      = {{Journal of Computational and Applied Mathematics}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  publisher    = {{Elsevier BV}},
  title        = {{{Local RBF-based penalized least-squares approximation on the sphere with noisy scattered data}}},
  doi          = {{10.1016/j.cam.2020.113061}},
  volume       = {{382}},
  year         = {{2021}},
}

@article{34840,
  abstract     = {{In this paper we obtain a complete list of imaginary n-quadratic fields with class groups of exponent 3 and 5 under ERH for every positive integer n where an n-quadratic field is a number field of degree 2ⁿ represented as the composite of n quadratic fields. }},
  author       = {{Klüners, Jürgen and Komatsu, Toru}},
  issn         = {{0025-5718}},
  journal      = {{Mathematics of Computation}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Algebra and Number Theory}},
  number       = {{329}},
  pages        = {{1483--1497}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{Imaginary multiquadratic number fields with class group of exponent $3$ and $5$}}},
  doi          = {{10.1090/mcom/3609}},
  volume       = {{90}},
  year         = {{2021}},
}

@article{34912,
  abstract     = {{Let E be an ordinary elliptic curve over a finite field and g be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in the isogeny class of E⁹ . The varieties are first described as hermitian lattices over (not necessarily maximal) quadratic orders and then geometrically in terms of their algebraic theta null point. We also show how to algebraically compute Siegel modular forms of even weight given as polynomials in the theta constants by a careful choice of an affine lift of the theta null point. We then use these results to give an algebraic computation of Serre’s obstruction for principally polarized abelian threefolds isogenous to E³ and of the Igusa modular form in dimension 4. We illustrate our algorithms with examples of curves with many rational points over finite fields. }},
  author       = {{Kirschmer, Markus and Narbonne, Fabien and Ritzenthaler, Christophe and Robert, Damien}},
  issn         = {{0025-5718}},
  journal      = {{Mathematics of Computation}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Algebra and Number Theory}},
  number       = {{333}},
  pages        = {{401--449}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{Spanning the isogeny class of a power of an elliptic curve}}},
  doi          = {{10.1090/mcom/3672}},
  volume       = {{91}},
  year         = {{2021}},
}

@article{40250,
  author       = {{Jain, Mitisha and Gerstmann, Uwe and Schmidt, Wolf Gero and Aldahhak, Hazem}},
  issn         = {{0192-8651}},
  journal      = {{Journal of Computational Chemistry}},
  keywords     = {{Computational Mathematics, General Chemistry}},
  number       = {{6}},
  pages        = {{413--420}},
  publisher    = {{Wiley}},
  title        = {{{Adatom mediated adsorption of            <scp>N‐heterocyclic</scp>            carbenes on Cu(111) and Au(111)}}},
  doi          = {{10.1002/jcc.26801}},
  volume       = {{43}},
  year         = {{2021}},
}

@article{45954,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>$L^2$ norm error estimates of semi- and full discretizations of wave equations with dynamic boundary conditions, using bulk–surface finite elements and Runge–Kutta methods, are studied. The analysis rests on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed, which fit into the abstract framework. For problems with velocity terms or with acoustic boundary conditions we prove surprising results: for such problems the spatial convergence order is shown to be less than 2. These can also be observed in the presented numerical experiments.</jats:p>}},
  author       = {{Hipp, David and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{1}},
  pages        = {{638--728}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates}}},
  doi          = {{10.1093/imanum/drz073}},
  volume       = {{41}},
  year         = {{2020}},
}

@article{45953,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>$L^2$ norm error estimates of semi- and full discretizations of wave equations with dynamic boundary conditions, using bulk–surface finite elements and Runge–Kutta methods, are studied. The analysis rests on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed, which fit into the abstract framework. For problems with velocity terms or with acoustic boundary conditions we prove surprising results: for such problems the spatial convergence order is shown to be less than 2. These can also be observed in the presented numerical experiments.</jats:p>}},
  author       = {{Hipp, David and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{1}},
  pages        = {{638--728}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates}}},
  doi          = {{10.1093/imanum/drz073}},
  volume       = {{41}},
  year         = {{2020}},
}

@article{45955,
  author       = {{Akrivis, Georgios and Feischl, Michael and Kovács, Balázs and Lubich, Christian}},
  issn         = {{0025-5718}},
  journal      = {{Mathematics of Computation}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Algebra and Number Theory}},
  number       = {{329}},
  pages        = {{995--1038}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation}}},
  doi          = {{10.1090/mcom/3597}},
  volume       = {{90}},
  year         = {{2020}},
}

@article{33866,
  abstract     = {{<jats:p>Helhmoltz–Kirchhoff equations of motions of vortices of an incompressible fluid in the plane define a dynamics with singularities and this leads to a Zermelo navigation problem describing the ship travel in such a field where the control is the heading angle. Considering one vortex, we define a time minimization problem which can be analyzed with the technics of geometric optimal control combined with numerical simulations, the geometric frame being the extension of Randers metrics in the punctured plane, with rotational symmetry. Candidates as minimizers are parameterized thanks to the Pontryagin Maximum Principle as extremal solutions of a Hamiltonian vector field. We analyze the time minimal solution to transfer the ship between two points where during the transfer the ship can be either in a strong current region in the vicinity of the vortex or in a weak current region. The analysis is based on a micro-local classification of the extremals using mainly the integrability properties of the dynamics due to the rotational symmetry. The discussion is complex and related to the existence of an isolated extremal (Reeb) circle due to the vortex singularity. The explicit computation of cut points where the extremal curves cease to be optimal is given and the spheres are described in the case where at the initial point the current is weak.</jats:p>}},
  author       = {{Bonnard, Bernard and Cots, Olivier and Wembe Moafo, Boris Edgar}},
  issn         = {{1292-8119}},
  journal      = {{ESAIM: Control, Optimisation and Calculus of Variations}},
  keywords     = {{Computational Mathematics, Control and Optimization, Control and Systems Engineering}},
  publisher    = {{EDP Sciences}},
  title        = {{{A Zermelo navigation problem with a vortex singularity}}},
  doi          = {{10.1051/cocv/2020058}},
  volume       = {{27}},
  year         = {{2020}},
}

@article{34669,
  author       = {{Black, Tobias}},
  issn         = {{1422-6928}},
  journal      = {{Journal of Mathematical Fluid Mechanics}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Condensed Matter Physics, Mathematical Physics}},
  number       = {{1}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System}}},
  doi          = {{10.1007/s00021-019-0464-z}},
  volume       = {{22}},
  year         = {{2019}},
}

@article{45948,
  author       = {{Kovács, Balázs and Li, Buyang and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{4}},
  pages        = {{797--853}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A convergent evolving finite element algorithm for mean curvature flow of closed surfaces}}},
  doi          = {{10.1007/s00211-019-01074-2}},
  volume       = {{143}},
  year         = {{2019}},
}

@article{34664,
  author       = {{Black, Tobias}},
  issn         = {{0036-1410}},
  journal      = {{SIAM Journal on Mathematical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Analysis}},
  number       = {{4}},
  pages        = {{4087--4116}},
  publisher    = {{Society for Industrial & Applied Mathematics (SIAM)}},
  title        = {{{Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion}}},
  doi          = {{10.1137/17m1159488}},
  volume       = {{50}},
  year         = {{2018}},
}

@article{33261,
  abstract     = {{We prove that steady state bifurcations in finite-dimensional dynamical systems that are symmetric with respect to a monoid representation generically occur along an absolutely indecomposable subrepresentation. This is stated as a conjecture in [B. Rink and J. Sanders, SIAM J. Math. Anal., 46 (2014), pp. 1577--1609]. It is a generalization of the well-known fact that generic steady state bifurcations in equivariant dynamical systems occur along an absolutely irreducible subrepresentation if the symmetries form a group---finite or compact Lie. Our generalization also includes noncompact symmetry groups. The result has applications in bifurcation theory of homogeneous coupled cell networks as they can be embedded (under mild additional assumptions) into monoid equivariant systems.}},
  author       = {{Schwenker, Sören}},
  issn         = {{0036-1410}},
  journal      = {{SIAM Journal on Mathematical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Analysis}},
  number       = {{3}},
  pages        = {{2466--2485}},
  publisher    = {{Society for Industrial & Applied Mathematics (SIAM)}},
  title        = {{{Generic Steady State Bifurcations in Monoid Equivariant Dynamics with Applications in Homogeneous Coupled Cell Systems}}},
  doi          = {{10.1137/17m116118x}},
  volume       = {{50}},
  year         = {{2018}},
}

@article{45950,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>The maximum principle forms an important qualitative property of second-order elliptic equations; therefore, its discrete analogues, the so-called discrete maximum principles (DMPs), have drawn much attention owing to their role in reinforcing the qualitative reliability of the given numerical scheme. In this paper DMPs are established for nonlinear finite element problems on surfaces with boundary, corresponding to the classical pointwise maximum principles on Riemannian manifolds in the spirit of Pucci &amp; Serrin (2007, The Maximum Principle. Springer). Various real-life examples illustrate the scope of the results.</jats:p>}},
  author       = {{Karátson, János and Kovács, Balázs and Korotov, Sergey}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{2}},
  pages        = {{1241--1265}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary}}},
  doi          = {{10.1093/imanum/dry086}},
  volume       = {{40}},
  year         = {{2018}},
}

@article{45949,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>The maximum principle forms an important qualitative property of second-order elliptic equations; therefore, its discrete analogues, the so-called discrete maximum principles (DMPs), have drawn much attention owing to their role in reinforcing the qualitative reliability of the given numerical scheme. In this paper DMPs are established for nonlinear finite element problems on surfaces with boundary, corresponding to the classical pointwise maximum principles on Riemannian manifolds in the spirit of Pucci &amp; Serrin (2007, The Maximum Principle. Springer). Various real-life examples illustrate the scope of the results.</jats:p>}},
  author       = {{Karátson, János and Kovács, Balázs and Korotov, Sergey}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{2}},
  pages        = {{1241--1265}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary}}},
  doi          = {{10.1093/imanum/dry086}},
  volume       = {{40}},
  year         = {{2018}},
}