# Article

 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 . 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