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Bubbles Enriched Quadratic Finite Element Method for the 3D-Elliptic Obstacle Problem

Gaddam, Sharat and Gudi, Thirupathi (2018) Bubbles Enriched Quadratic Finite Element Method for the 3D-Elliptic Obstacle Problem. In: COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 18 (2). pp. 223-236.

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Official URL: http://dx.doi.org/10.1515/cmam-2017-0018

Abstract

An optimally convergent (with respect to the regularity) quadratic finite element method for the two-dimensional obstacle problem on simplicial meshes is studied in 14]. There was no analogue of a quadratic finite element method on tetrahedron meshes for the three-dimensional obstacle problem. In this article, a quadratic finite element enriched with element-wise bubble functions is proposed for the three-dimensional elliptic obstacle problem. A priori error estimates are derived to show the optimal convergence of the method with respect to the regularity. Further, a posteriori error estimates are derived to design an adaptive mesh refinement algorithm. A numerical experiment illustrating the theoretical result on a priori error estimates is presented.

Item Type: Journal Article
Additional Information: Copy right for this article belong to WALTER DE GRUYTER GMBH, GENTHINER STRASSE 13, D-10785 BERLIN, GERMANY
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 14 Apr 2018 18:50
Last Modified: 14 Apr 2018 18:50
URI: http://eprints.iisc.ac.in/id/eprint/59569

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