arXiv subjects

Mária Lukáčová-Medvidová

Publications and source records attributed to Mária Lukáčová-Medvidová.

2 recordsLinked to original sources

arXiv2026

Structure-preserving approximation of the non-isothermal Cahn-Hilliard system based on the entropy equation

We propose and analyze a structure-preserving approximation of the non-isothermal Cahn-Hilliard equation using conforming finite elements for the spatial discretization and a problem-specific mixed explicit-implicit approach for the temporal discretization. To ensure the preservation of structural properties, i.e. conservation of mass and internal energy as well as entropy production, we introduce a suitable variational formulation for the continuous problem, based on the entropy equation. Analytical findings are supported by numerical tests, including convergence analysis.

math.NA↗

arXiv2025

Convergence analysis for a finite volume evolution Galerkin method for multidimensional hyperbolic systems

We study the convergence of a finite volume method based on the method of bicharacteristics for multidimensional hyperbolic conservation laws. In particular, we concentrate on the linear wave equation system and nonlinear Euler equations of gas dynamics. We show the stability and the consistency of the numerical approximations. By means of the generalized Lax equivalence principle we prove the convergence of numerical solutions to the strong solution on the lifespan.

math.NA↗