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# Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Volume 18, Issue 2

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

Sharat Gaddam
/ Thirupathi Gudi
Published Online: 2017-07-11 | DOI: https://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.

MSC 2010: 65N30; 65N15; 65N12

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## About the article

Received: 2016-11-03

Revised: 2017-04-10

Accepted: 2017-06-07

Published Online: 2017-07-11

Published in Print: 2018-04-01

Citation Information: Computational Methods in Applied Mathematics, Volume 18, Issue 2, Pages 223–236, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840,

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© 2018 Walter de Gruyter GmbH, Berlin/Boston.

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