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Title: Verification of functional a posteriori error estimates for obstacle problem in 2D (English)
Author: Harasim, Petr
Author: Valdman, Jan
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 50
Issue: 6
Year: 2014
Pages: 978-1002
Summary lang: English
Category: math
Summary: We verify functional a posteriori error estimates proposed by S. Repin for a class of obstacle problems in two space dimensions. New benchmarks with known analytical solution are constructed based on one dimensional benchmark introduced by P. Harasim and J. Valdman. Numerical approximation of the solution of the obstacle problem is obtained by the finite element method using bilinear elements on a rectangular mesh. Error of the approximation is measured by a functional majorant. The majorant value contains three unknown fields: a gradient field discretized by Raviart-Thomas elements, Lagrange multipliers field discretized by piecewise constant functions and a scalar parameter $\beta$. The minimization of the majorant value is realized by an alternate minimization algorithm, whose convergence is discussed. Numerical results validate two estimates, the energy estimate bounding the error of approximation in the energy norm by the difference of energies of discrete and exact solutions and the majorant estimate bounding the difference of energies of discrete and exact solutions by the value of the functional majorant. (English)
Keyword: obstacle problem
Keyword: a posteriori error estimate
Keyword: functional majorant
Keyword: finite element method
Keyword: variational inequalities
Keyword: Raviart–Thomas elements
MSC: 34B15
MSC: 65K15
MSC: 65L60
MSC: 74K05
MSC: 74M15
MSC: 74S05
idZBL: Zbl 06416870
idMR: MR3301782
DOI: 10.14736/kyb-2014-6-0978
Date available: 2015-01-13T10:00:44Z
Last updated: 2016-01-03
Stable URL:
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