Balázs Kovács

Codes for all publications are available via GitLab, or upon request.

Preprints

• B. Kovács. Numerical surgery for mean curvature flow of surfaces. October 2022.
• S. Bartels, B. Kovács, and Z. Wang. Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints. August 2022.
• H. Garcke, B. Kovács, and D. Trautwein. Viscoelastic Cahn–Hilliard models for tumour growth. April 2022, revised September 2022. To appear in M3AS, 2022. [arXiv]
• P. Csomós, B. Farkas, and B. Kovács. Error estimates for a splitting integrator for abstract semilinear boundary coupled systems. December 2021, revised April, October, and November 2022. To appear in IMA Journal of Numerical Analysis, 2023. [arXiv]
• R. Altmann, B. Kovács, and C. Zimmer. Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions. August 2021, revised January 2022. To appear in IMA Journal of Numerical Analysis, 2022. [arXiv]
• T. Binz and B. Kovács. A convergent finite element algorithm for mean curvature flow in arbitrary codimension. July 2021, revised February, July 2022.
• B. Kovács and B. Li. Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems. June 2021, revised January 2022. To appear in IMA Journal of Numerical Analysis, 2022. [arXiv]
• J. Bohn, M. Feischl, and B. Kovács. FEM–BEM coupling for Maxwell–Landau–Lifshitz–Gilbert equations via convolution quadrature: Weak form and numerical approximation. March 2020, revised May 2020, October 2021, September 2022. To appear in Computational Methods in Applied Mathematics, 2022.

Papers

• P. Harder and B. Kovács. Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions. IMA Journal of Numerical Analysis, 42(3):2589–2620, 2022. [arXiv]
• T. Binz and B. Kovács. A convergent finite element algorithm for generalized mean curvature flows of closed surfaces. IMA Journal of Numerical Analysis, 42(3):2545–2588, 2022. [arXiv]
• C. M. Elliott, H. Garcke, and B. Kovács. Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. Numerische Mathematik, 151(4):873–925, 2022. [arXiv]
• C. A. Beschle and B. Kovács. Error estimates for generalised non-linear Cahn–Hilliard equations on evolving surfaces. Numerische Mathematik, 151(1):1–48, 2022. [arXiv]
• J. Nick, B. Kovács, and Ch. Lubich. Time-dependent electromagnetic scattering from thin layers. Numerische Mathematik 150(4):1123–1164, 2022. [arXiv]
• B. Kovács, B. Li, and Ch. Lubich. A convergent evolving finite element algorithm for Willmore flow of closed surfaces. Numerische Mathematik, 149(4):595–643, 2021. [arXiv]
• G. Akrivis, M. Feischl, B. Kovács, and Ch. Lubich. Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation. Mathematics of Computation, 90(329):995–1038, 2021. [arXiv]
• J. Nick, B. Kovács, and Ch. Lubich, Correction to: Stable and convergent fully discrete interior-exterior coupling of Maxwell's equations. Numerische Mathematik, 147:997–1000, 2021.
• D. Hipp and B. Kovács. Finite element error analysis of wave equations with dynamic boundary conditions: \(L^2\) estimates. IMA Journal of Numerical Analysis, 41(1):683–728, 2021.
• B. Kovács, B. Li, and Ch. Lubich. A convergent algorithm for forced mean curvature flow driven by diffusion on the surface. Interfaces and Free Boundaries, 22(4):443–464, 2020. [arXiv]
• J. Karátson, B. Kovács, and S. Korotov. Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary. IMA Journal of Numerical Analysis, 40(2):1241–1265, 2020.
• B. Kovács, B. Li, and Ch. Lubich. A convergent evolving finite element algorithm for mean curvature flow of closed surfaces. Numerische Mathematik, 143(4):797–853, 2019.
• B. Kovács. Computing arbitrary Lagrangian Eulerian maps for evolving surfaces. NMPDE, 35(3):1093–1112, 2019.
• B. Kovács and Ch. Lubich. Linearly implicit full discretization of surface evolution. Numerische Mathematik, 140(1):121–152, 2018.
• B. Kovács and C.A. Power Guerra. Maximum norm stability and error estimates for the evolving surface finite element method. NMPDE, 34(2):518–554, 2018.
• B. Kovács and C.A. Power Guerra. Higher-order time discretizations with ALE finite elements for parabolic problems on evolving surfaces. IMA Journal of Numerical Analysis, 38(1):460–494, 2018.
• B. Kovács. High-order evolving surface finite element method for parabolic problems on evolving surfaces. IMA Journal of Numerical Analysis, 38(1):430–459, 2018.
• B. Kovács and Ch. Lubich. Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type. Numerische Mathematik, 138(2):365–388, 2018.
• B. Kovács, B. Li, Ch. Lubich, and C.A. Power Guerra. Convergence of finite elements on an evolving surface driven by diffusion on the surface.Numerische Mathematik, 137(3):643–689, 2017.
• B. Kovács and Ch. Lubich. Stable and convergent fully discrete interior–exterior coupling of Maxwell's equations. Numerische Mathematik, 137(1):91–117, 2017.
• B. Kovács and Ch. Lubich. Numerical analysis of parabolic problems with dynamic boundary conditions. IMA Journal of Numerical Analysis, 37(1):1–39, 2017.
• B. Kovács, B. Li, and Ch. Lubich. A-stable time discretizations preserve maximal parabolic regularity. SIAM Journal on Numerical Analysis, 54(6):3600–3624, 2016.
• J. Karátson and B. Kovács. A parallel numerical solution approach for nonlinear parabolic systems arising in air pollution transport problems. In Mathematical Problems in Meteorological Modelling, pages 57–70. Springer International Publishing, 2016.
• B. Kovács and C.A. Power Guerra. Error analysis for full discretizations of quasilinear parabolic problems on evolving surfaces. NMPDE, 32(4):1200–1231, 2016.
• O. Axelsson, J. Karátson, and B. Kovács. Robust preconditioning estimates for convection-dominated elliptic problems via a streamline Poincaré–Friedrichs inequality. SIAM Journal on Numerical Analysis, 52(6):2957– 2976, 2014.
• B. Kovács. On the numerical performance of a sharp a posteriori error estimator for some nonlinear elliptic problems. Applications of Mathematics, 59(5):489–508, 2014.
• J. Karátson and B. Kovács. Variable preconditioning in complex Hilbert space and its application to the nonlinear Schrödinger equation. Computers Mathematics with Applications, 65(3):449–459, 2013.
• B. Kovács. A comparison of some efficient numerical methods for a nonlinear elliptic problem. Central European Journal of Mathematics, 10(1):217–230, 2012.

Theses

[T2] B. Kovács. Numerical analysis of partial differential equations on and of evolving surfaces. Habilitation thesis. University of Tübingen, Tübingen, Germany. December 2018.

[T1] B. Kovács. Efficient numerical methods for elliptic and parabolic partial differential equations. PhD thesis. ELTE Eötvös Loránd University, Budapest, Hungary. 2015.