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Inhomogeneous Dirichlet boundary condition in the a posteriori error control of the obstacle problem

Gaddam, Sharat and Gudi, Thirupathi (2018) Inhomogeneous Dirichlet boundary condition in the a posteriori error control of the obstacle problem. In: COMPUTERS & MATHEMATICS WITH APPLICATIONS, 75 (7). pp. 2311-2327.

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Official URL: http://dx.doi.org/10.1016/j.camwa.2017.12.010

Abstract

We study a posteriori error control of finite element approximation of the elliptic obstacle problem with nonhomogeneous Dirichlet boundary condition. The results in the article are two fold. Firstly, we address the influence of the inhomogeneous Dirichlet boundary condition in residual based a posteriori error control of the elliptic obstacle problem. Secondly by rewriting the obstacle problem in an equivalent form, we derive a posteriori error bounds which are in simpler form and efficient. To accomplish this, we construct and use a post-processed solution (u) over tilde (h) of the discrete solution u(h) which satisfies the exact boundary conditions sharply although the discrete solution u(h) may not satisfy. We propose two post processing methods and analyze them, namely the harmonic extension and a linear extension. The theoretical results are illustrated by the numerical results. (C) 2017 Elsevier Ltd. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belong to PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 04 May 2018 18:47
Last Modified: 04 May 2018 18:47
URI: http://eprints.iisc.ac.in/id/eprint/59759

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