The variable-order discontinuous Galerkin time stepping scheme for parabolic evolution problems is uniformly L^∞-stable

2017/11/27 by Lars Schmutz, Thomas P. Wihler, Schmutz, Lars +1
Computer Science · Engineering · Mathematics · #65J08 #65M12 #65M60 #65M70 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1711.09650

openalex publication_date 2017/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate the L^∞-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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