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Adaptive discontinuous galerkin approximations to fourth order parabolic problems

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journal contribution
posted on 01.10.2019, 14:25 by Emmanuil H. Georgoulis, Juha M. Virtanen
An adaptive algorithm, based on residual type a posteriori indicators of errors measured in L < sup > ∞ < /sup > (L < sup > 2 < /sup > ) and L < sup > 2 < /sup > (L < sup > 2 < /sup > ) norms, for a numerical scheme consisting of implicit Euler method in time and discontinuous Galerkin method in space for linear parabolic fourth order problems is presented. The a posteriori analysis is performed for convex domains in two and three space dimensions for local spatial polynomial degrees r ≥ 2. The a posteriori estimates are then used within an adaptive algorithm, highlighting their relevance in practical computations, by resulting in substantial reduction of computational effort.

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Citation

Mathematics of Computation, 2015, 84 (295), pp. 2163-2190

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

AM (Accepted Manuscript)

Published in

Mathematics of Computation

Publisher

American Mathematical Society

issn

0025-5718

Copyright date

2015

Available date

01/10/2019

Publisher version

https://www.ams.org/journals/mcom/2015-84-295/S0025-5718-2015-02936-6/home.html

Language

en

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