The variable-order discontinuous Galerkin time stepping scheme for parabolic evolution problems is uniformly $\mathrm{L}^\infty$-stable
Numerical Analysis
2017-11-28 v1
Abstract
In this paper we investigate the -stability of fully discrete approximations of abstract linear parabolic partial differential equations. The method under consideration is based on an -type discontinuous Galerkin time stepping scheme in combination with general conforming Galerkin discretizations in space. Our main result shows that the global-in-time maximum norm of the discrete solution is bounded by the data of the PDE, with a constant that is robust with respect to the discretization parameters (in particular, it is uniformly bounded with respect to the local time steps and approximation orders).
Cite
@article{arxiv.1711.09650,
title = {The variable-order discontinuous Galerkin time stepping scheme for parabolic evolution problems is uniformly $\mathrm{L}^\infty$-stable},
author = {Lars Schmutz and Thomas P. Wihler},
journal= {arXiv preprint arXiv:1711.09650},
year = {2017}
}