Conditional a posteriori error bounds for high order discontinuous Galerkin time stepping approximations of semilinear heat models with blow-up.

Metcalfe, Stephen; Wihler, Thomas P. (2022). Conditional a posteriori error bounds for high order discontinuous Galerkin time stepping approximations of semilinear heat models with blow-up. SIAM Journal on Scientific Computing, 44(3), A1337-A1357. Society for Industrial and Applied Mathematics 10.1137/21M1418964

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This work is concerned with the development of an adaptive numerical method for semilinear heat flow models featuring a general (possibly) nonlinear reaction term that may cause the solution to blow up in finite time. The fully discrete scheme consists of a high order discontinuous Galerkin time stepping method and a conforming finite element discretization in space. The proposed adaptive procedure is based on rigorously devised conditional a posteriori error bounds in the L∞(L∞) norm. Numerical experiments complement the theoretical results; in particular, we investigate whether exponential convergence to the blow-up time can be achieved via hp-adaptivity.

Item Type:	Journal Article (Original Article)
Division/Institute:	08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics
UniBE Contributor:	Wihler, Thomas
Subjects:	500 Science > 510 Mathematics
ISSN:	1064-8275
Publisher:	Society for Industrial and Applied Mathematics
Funders:	Organisations 200021 not found.
Language:	English
Submitter:	Zarif Ibragimov
Date Deposited:	21 Feb 2023 07:36
Last Modified:	21 Feb 2023 23:27
Publisher DOI:	10.1137/21M1418964
URI:	https://boris.unibe.ch/id/eprint/178964