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Title: Computing upper bounds on Friedrichs’ constant (English)
Author: Vejchodský, Tomáš
Language: English
Journal: Applications of Mathematics 2012
Volume: Proceedings. Prague, May 2-5, 2012
Issue: 2012
Pages: 278-289
Category: math
Summary: This contribution shows how to compute upper bounds of the optimal constant in Friedrichs' and similar inequalities. The approach is based on the method of $a priori-a posteriori inequalities$ [9]. However, this method requires trial and test functions with continuous second derivatives. We show how to avoid this requirement and how to compute the bounds on Friedrichs' constant using standard finite element methods. This approach is quite general and allows variable coefficients and mixed boundary conditions. We use the computed upper bound on Friedrichs' constant in a posteriori error estimation to obtain guaranteed error bounds. (English)
Keyword: second-order boundary value problems
Keyword: a posteriori error estimates
Keyword: complementary energy
Keyword: Friedrichs’ inequality
Keyword: numerical example
MSC: 35A23
MSC: 35J25
MSC: 65N15
MSC: 65N30
idZBL: Zbl 1313.65296
idMR: MR3204419
Date available: 2017-02-14T09:04:37Z
Last updated: 2017-04-13
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