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New Error Estimates of Nonconforming Finite Element Methods for the Poisson Problem with Low Regularity Solution

Published online by Cambridge University Press:  03 June 2015

Youai Li
Youai Li*
Affiliation:
School of Science, Beijing Technology and Business University, Beijing 100048, China
*
*Corresponding author. Email: lya@lsec.cc.ac.cn
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Abstract

In this paper, we revisit a priori error analysis of nonconforming finite element methods for the Poisson problem. Based on some techniques developed in the context of the a posteriori error analysis, under two reasonable assumptions on the nonconforming finite element spaces, we prove that, up to some oscillation terms, the consistency error can be bounded by the approximation error. We check these two assumptions for the most used lower order nonconforming finite element methods. Compared with the classical error analysis of the nonconforming finite element method, the a priori analysis herein only needs the H1 regularity of the exact solution.

Keywords

65N3065N1535J25Error estimatenonconforming finite elementbubble functionPoisson problemlow regularity
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 2 , April 2014 , pp. 179 - 190
Copyright
Copyright © Global-Science Press 2014

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