Schmutz, Lars; Wihler, Thomas (2019). The variable-order discontinuous Galerkin time stepping scheme for parabolic evolution problems is uniformly L∞-stable. Siam journal on numerical analysis, 57(1), pp. 293-319. Society for Industrial and Applied Mathematics 10.1137/17M1158835
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In this paper we investigate the L∞-stability of fully discrete approximations of abstract linear parabolic partial differential equations (PDEs). 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).
Item Type: |
Journal Article (Original Article) |
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Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Schmutz, Lars, Wihler, Thomas |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
1095-7170 |
Publisher: |
Society for Industrial and Applied Mathematics |
Funders: |
[4] Swiss National Science Foundation |
Language: |
English |
Submitter: |
Michel Arthur Bik |
Date Deposited: |
06 Aug 2019 14:07 |
Last Modified: |
20 Dec 2023 11:40 |
Publisher DOI: |
10.1137/17M1158835 |
BORIS DOI: |
10.7892/boris.132260 |
URI: |
https://boris.unibe.ch/id/eprint/132260 |
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