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A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem

Gudi, Thirupathi and Porwal, Kamana (2015) A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem. In: COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 15 (2). pp. 145-160.

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Official URL: http://dx.doi.org/10.1515/cmam-2015-0005

Abstract

A residual based a posteriori error estimator is derived for a quadratic finite element method (FEM) for the elliptic obstacle problem. The error estimator involves various residuals consisting of the data of the problem, discrete solution and a Lagrange multiplier related to the obstacle constraint. The choice of the discrete Lagrange multiplier yields an error estimator that is comparable with the error estimator in the case of linear FEM. Further, an a priori error estimate is derived to show that the discrete Lagrange multiplier converges at the same rate as that of the discrete solution of the obstacle problem. The numerical experiments of adaptive FEM show optimal order convergence. This demonstrates that the quadratic FEM for obstacle problem exhibits optimal performance.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the WALTER DE GRUYTER GMBH, GENTHINER STRASSE 13, D-10785 BERLIN, GERMANY
Keywords: Finite Element; Quadratic FEM; A Posteriori Error Estimate; Obstacle Problem; Optimal Error Estimates; Variational Inequalities; Lagrange Multiplier
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 31 Jul 2015 13:33
Last Modified: 31 Jul 2015 13:33
URI: http://eprints.iisc.ac.in/id/eprint/51962

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