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

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)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Schmutz, Lars and Wihler, Thomas

Subjects:

500 Science > 510 Mathematics

ISSN:

1095-7170

Publisher:

Society for Industrial and Applied Mathematics

Language:

English

Submitter:

Michel Arthur Bik

Date Deposited:

06 Aug 2019 14:07

Last Modified:

23 Oct 2019 04:50

Publisher DOI:

10.1137/17M1158835

BORIS DOI:

10.7892/boris.132260

URI:

https://boris.unibe.ch/id/eprint/132260

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