Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary - Karátson, János; Kovács, Balázs; Korotov, Sergey (IMA Journal of Numerical Analysis)
Abstract 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 & Serrin (2007, The Maximum Principle. Springer). Various real-life examples illustrate the scope of the results.
Keywords: Applied Mathematics; Computational Mathematics; General Mathematics

Linearly implicit full discretization of surface evolution - Kovács, Balázs; Lubich, Christian (Numerische Mathematik)
Keywords: Applied Mathematics; Computational Mathematics

Computing arbitrary Lagrangian Eulerian maps for evolving surfaces - Kovács, Balázs (Numerical Methods for Partial Differential Equations)
Keywords: Applied Mathematics; Computational Mathematics; Numerical Analysis; Analysis

Radial basis function approximation of noisy scattered data on the sphere - Hesse, Kerstin; Sloan, Ian H.; Womersley, Robert S. (Numerische Mathematik)
Keywords: Applied Mathematics; Computational Mathematics

Convergence of finite elements on an evolving surface driven by diffusion on the surface - Kovács, Balázs; Li, Buyang; Lubich, Christian; Power Guerra, Christian A. (Numerische Mathematik)
Keywords: Applied Mathematics; Computational Mathematics

Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type - Kovács, Balázs; Lubich, Christian (Numerische Mathematik)
Keywords: Applied Mathematics; Computational Mathematics

Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations - Kovács, Balázs; Lubich, Christian (Numerische Mathematik)
Keywords: Applied Mathematics; Computational Mathematics

Maximum norm stability and error estimates for the evolving surface finite element method - Kovács, Balázs; Power Guerra, Christian Andreas (Numerical Methods for Partial Differential Equations)
Keywords: Applied Mathematics; Computational Mathematics; Numerical Analysis; Analysis

High-order evolving surface finite element method for parabolic problems on evolving surfaces - Kovács, Balázs (IMA Journal of Numerical Analysis)
Keywords: Applied Mathematics; Computational Mathematics; General Mathematics

Maximum norm stability and error estimates for the evolving surface finite element method - Kovács, Balázs; Power Guerra, Christian Andreas (Numerical Methods for Partial Differential Equations)
Keywords: Applied Mathematics; Computational Mathematics; Numerical Analysis; Analysis

Sublinear signal production in a two-dimensional Keller–Segel–Stokes system - Black, Tobias (Nonlinear Analysis: Real World Applications)
Keywords: Applied Mathematics; Computational Mathematics; General Economics; Econometrics and Finance; General Engineering; General Medicine; Analysis

Higher order time discretizations with ALE finite elements for parabolic problems on evolving surfaces - Kovács, Balázs; Power Guerra, Christian Andreas (IMA Journal of Numerical Analysis)
Keywords: Applied Mathematics; Computational Mathematics; General Mathematics

Error analysis for full discretizations of quasilinear parabolic problems on evolving surfaces - Kovács, Balázs; Power Guerra, Christian Andreas (Numerical Methods for Partial Differential Equations)
Keywords: Applied Mathematics; Computational Mathematics; Numerical Analysis; Analysis

A-Stable Time Discretizations Preserve Maximal Parabolic Regularity - Kovács, Balázs; Li, Buyang; Lubich, Christian (SIAM Journal on Numerical Analysis)
Keywords: Numerical Analysis; Applied Mathematics; Computational Mathematics

Numerical analysis of parabolic problems with dynamic boundary conditions - Kovács, Balázs; Lubich, Christian (IMA Journal of Numerical Analysis)
Keywords: Applied Mathematics; Computational Mathematics; General Mathematics

Robust Preconditioning Estimates for Convection-Dominated Elliptic Problems via a Streamline Poincaré--Friedrichs Inequality - Axelsson, Owe; Karátson, János; Kovács, Balázs (SIAM Journal on Numerical Analysis)
Keywords: Numerical Analysis; Applied Mathematics; Computational Mathematics

Increasing the Dimensionality of Quantum Walks Using Multiple Walkers - Rohde, Peter P.; Schreiber, Andreas; Štefaňák, Martin; Jex, Igor; Gilchrist, Alexei; Silberhorn, Christine (Journal of Computational and Theoretical Nanoscience)
Keywords: Electrical and Electronic Engineering; Computational Mathematics; Condensed Matter Physics; General Materials Science; General Chemistry

A normal form for definite quadratic forms over $\mathbb{F}_{q}[t]$ - Kirschmer, Markus (Mathematics of Computation)
An efficient algorithm to compute automorphism groups and isometries of definite Fq[t]-lattices for odd q is presented. The algorithm requires several square root computations in Fq₂ but no enumeration of orbits having more than eight elements.
Keywords: Applied Mathematics; Computational Mathematics; Algebra and Number Theory

Variable preconditioning in complex Hilbert space and its application to the nonlinear Schrödinger equation - Karátson, J.; Kovács, Balázs (Computers & Mathematics with Applications)
Keywords: Computational Mathematics; Computational Theory and Mathematics; Modeling and Simulation

Generating subfields - van Hoeij, Mark; Klüners, Jürgen; Novocin, Andrew (Journal of Symbolic Computation)
Given a field extension K/k of degree n we are interested in finding the subfields of K containing k. There can be more than polynomially many subfields. We introduce the notion of generating subfields, a set of up to n subfields whose intersections give the rest. We provide an efficient algorithm which uses linear algebra in k or lattice reduction along with factorization in any extension of K. Implementations show that previously difficult cases can now be handled.
Keywords: Computational Mathematics; Algebra and Number Theory