Structure-preserving discontinuous Galerkin approximation of a hyperbolic-parabolic system
Publication date
2025-01-15
Document type
Forschungsartikel
Author
Organisational unit
Publisher
Kent State University
Series or journal
Electronic transactions on numerical analysis
ISSN
Periodical volume
63
First page
1
Last page
32
Peer-reviewed
✅
Part of the university bibliography
✅
Language
English
Abstract
We study the numerical approximation of a coupled hyperbolic-parabolic system by a family of discontinuous Galerkin (DG) space-time finite element methods. The model is rewritten as a first-order evolutionary problem that is treated by a unified abstract solution theory. For the discretization in space, generalizations of the distribution gradient and divergence operators on broken polynomial spaces are defined. Since their skew-selfadjointness is perturbed by boundary surface integrals, adjustments are introduced such that the skew-selfadjointness of the discrete counterpart of the total system’s first-order differential operator in space is recovered. Well-posedness of the fully discrete problem and error estimates for the DG approximation in space and time are proved.
Description
This work is licenced under the Creative Commons licence CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/).
Version
Published version
Access right on openHSU
Metadata only access