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Accessible Unlicensed Requires Authentication Published by De Gruyter March 10, 2015

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

Thirupathi Gudi and Kamana Porwal

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.

MSC: 65N30; 65N15

Funding source: DST Fast Track Project

Funding source: UGC Center for Advanced Study

Funding source: Council for Scientific and Industrial Research (CSIR)

The authors would like to acknowledge the fruitful discussions with Professor Carsten Carstensen and Professor Andreas Veeser.

Received: 2014-9-16
Revised: 2015-2-25
Accepted: 2015-2-26
Published Online: 2015-3-10
Published in Print: 2015-4-1

© 2015 by De Gruyter