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arXiv · 1711.09650

The variable-order discontinuous Galerkin time stepping scheme for parabolic evolution problems is uniformly $\mathrm{L}^\infty$-stable

Lars Schmutz·Thomas P. Wihler
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Abstract

In this paper we investigate the $\mathrm{L}^\infty$-stability of fully discrete approximations of abstract linear parabolic partial differential equations. The method under consideration is based on an $hp$-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).

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Lars Schmutz, Thomas P. Wihler. 2017-11-27. The variable-order discontinuous Galerkin time stepping scheme for parabolic evolution problems is uniformly $\mathrm{L}^\infty$-stable. https://arxiv.org/abs/1711.09650

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