@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}},
}

@misc{45974,
  author       = {{Kovács, Balázs}},
  title        = {{{Numerical analysis of partial differential equations on and of evolving surfaces}}},
  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{45947,
  author       = {{Kovács, Balázs and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{1}},
  pages        = {{121--152}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Linearly implicit full discretization of surface evolution}}},
  doi          = {{10.1007/s00211-018-0962-6}},
  volume       = {{140}},
  year         = {{2018}},
}

@article{45951,
  author       = {{Kovács, Balázs}},
  issn         = {{0749-159X}},
  journal      = {{Numerical Methods for Partial Differential Equations}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Numerical Analysis, Analysis}},
  number       = {{3}},
  pages        = {{1093--1112}},
  publisher    = {{Wiley}},
  title        = {{{Computing arbitrary Lagrangian Eulerian maps for evolving surfaces}}},
  doi          = {{10.1002/num.22340}},
  volume       = {{35}},
  year         = {{2018}},
}

@article{45941,
  author       = {{Kovács, Balázs and Li, Buyang and Lubich, Christian and Power Guerra, Christian A.}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{3}},
  pages        = {{643--689}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Convergence of finite elements on an evolving surface driven by diffusion on the surface}}},
  doi          = {{10.1007/s00211-017-0888-4}},
  volume       = {{137}},
  year         = {{2017}},
}

@article{45942,
  author       = {{Kovács, Balázs and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{2}},
  pages        = {{365--388}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type}}},
  doi          = {{10.1007/s00211-017-0909-3}},
  volume       = {{138}},
  year         = {{2017}},
}

@article{45940,
  author       = {{Kovács, Balázs and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{1}},
  pages        = {{91--117}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations}}},
  doi          = {{10.1007/s00211-017-0868-8}},
  volume       = {{137}},
  year         = {{2017}},
}

@article{45946,
  author       = {{Kovács, Balázs and Power Guerra, Christian Andreas}},
  issn         = {{0749-159X}},
  journal      = {{Numerical Methods for Partial Differential Equations}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Numerical Analysis, Analysis}},
  number       = {{2}},
  pages        = {{518--554}},
  publisher    = {{Wiley}},
  title        = {{{Maximum norm stability and error estimates for the evolving surface finite element method}}},
  doi          = {{10.1002/num.22212}},
  volume       = {{34}},
  year         = {{2017}},
}

@article{45943,
  author       = {{Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{1}},
  pages        = {{430--459}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{High-order evolving surface finite element method for parabolic problems on evolving surfaces}}},
  doi          = {{10.1093/imanum/drx013}},
  volume       = {{38}},
  year         = {{2017}},
}

@article{33260,
  abstract     = {{In this paper we continue the study of group representations which are counterexamples to the Ize conjecture. As in previous papers we find new infinite series of finite groups leading to such counterexamples. These new series are quite different from the previous ones, for example the group orders do not form an arithmetic progression. However, as before we find Lie groups which contain all these groups. This additional structure was observed, but not used in the previous studies of this problem. Here we also investigate the related bifurcations. To a large extent, these are closely related to the presence of mentioned compact Lie group containing the finite groups. This might give a tool to study the bifurcations related to all low dimensional counterexamples of the Ize conjecture. It also gives an indication of where we can expect to find examples where the bifurcation behaviour is different from what we have seen in the known examples.}},
  author       = {{Lauterbach, Reiner and Schwenker, Sören}},
  issn         = {{1468-9367}},
  journal      = {{Dynamical Systems}},
  keywords     = {{Computer Science Applications, General Mathematics}},
  number       = {{1}},
  pages        = {{117--147}},
  publisher    = {{Informa UK Limited}},
  title        = {{{Equivariant bifurcations in four-dimensional fixed point spaces}}},
  doi          = {{10.1080/14689367.2016.1219696}},
  volume       = {{32}},
  year         = {{2016}},
}

@article{45944,
  author       = {{Kovács, Balázs and Power Guerra, Christian Andreas}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{1}},
  pages        = {{460--494}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Higher order time discretizations with ALE finite elements for parabolic problems on evolving surfaces}}},
  doi          = {{10.1093/imanum/drw074}},
  volume       = {{38}},
  year         = {{2016}},
}

@article{45936,
  author       = {{Kovács, Balázs and Power Guerra, Christian Andreas}},
  issn         = {{0749-159X}},
  journal      = {{Numerical Methods for Partial Differential Equations}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Numerical Analysis, Analysis}},
  number       = {{4}},
  pages        = {{1200--1231}},
  publisher    = {{Wiley}},
  title        = {{{Error analysis for full discretizations of quasilinear parabolic problems on evolving surfaces}}},
  doi          = {{10.1002/num.22047}},
  volume       = {{32}},
  year         = {{2016}},
}

@article{45939,
  author       = {{Kovács, Balázs and Li, Buyang and Lubich, Christian}},
  issn         = {{0036-1429}},
  journal      = {{SIAM Journal on Numerical Analysis}},
  keywords     = {{Numerical Analysis, Applied Mathematics, Computational Mathematics}},
  number       = {{6}},
  pages        = {{3600--3624}},
  publisher    = {{Society for Industrial & Applied Mathematics (SIAM)}},
  title        = {{{A-Stable Time Discretizations Preserve Maximal Parabolic Regularity}}},
  doi          = {{10.1137/15m1040918}},
  volume       = {{54}},
  year         = {{2016}},
}

@article{45937,
  author       = {{Kovács, Balázs and Lubich, Christian}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{1}},
  pages        = {{1--39}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Numerical analysis of parabolic problems with dynamic boundary conditions}}},
  doi          = {{10.1093/imanum/drw015}},
  volume       = {{37}},
  year         = {{2016}},
}

@inproceedings{45938,
  author       = {{Karátson, J. and Kovács, Balázs}},
  booktitle    = {{Mathematical Problems in Meteorological Modelling}},
  pages        = {{57–70}},
  title        = {{{A Parallel Numerical Solution Approach for Nonlinear Parabolic Systems Arising in Air Pollution Transport Problems}}},
  year         = {{2016}},
}

@phdthesis{45973,
  author       = {{Kovács, Balázs}},
  title        = {{{Efficient numerical methods for elliptic and parabolic partial differential equations}}},
  doi          = {{10.15476/ELTE.2015.076}},
  year         = {{2015}},
}

@article{45934,
  author       = {{Kovács, Balázs}},
  issn         = {{0862-7940}},
  journal      = {{Applications of Mathematics}},
  keywords     = {{Applied Mathematics}},
  number       = {{5}},
  pages        = {{489--508}},
  publisher    = {{Institute of Mathematics, Czech Academy of Sciences}},
  title        = {{{On the numerical performance of a sharp a posteriori error estimator for some nonlinear elliptic problems}}},
  doi          = {{10.1007/s10492-014-0068-0}},
  volume       = {{59}},
  year         = {{2014}},
}

@article{45933,
  author       = {{Karátson, J. and Kovács, Balázs}},
  issn         = {{0898-1221}},
  journal      = {{Computers &amp; Mathematics with Applications}},
  keywords     = {{Computational Mathematics, Computational Theory and Mathematics, Modeling and Simulation}},
  number       = {{3}},
  pages        = {{449--459}},
  publisher    = {{Elsevier BV}},
  title        = {{{Variable preconditioning in complex Hilbert space and its application to the nonlinear Schrödinger equation}}},
  doi          = {{10.1016/j.camwa.2012.04.021}},
  volume       = {{65}},
  year         = {{2012}},
}

@article{45932,
  author       = {{Kovács, Balázs}},
  issn         = {{1895-1074}},
  journal      = {{Central European Journal of Mathematics}},
  keywords     = {{General Mathematics}},
  number       = {{1}},
  pages        = {{217--230}},
  publisher    = {{Walter de Gruyter GmbH}},
  title        = {{{A comparison of some efficient numerical methods for a nonlinear elliptic problem}}},
  doi          = {{10.2478/s11533-011-0071-6}},
  volume       = {{10}},
  year         = {{2011}},
}