Year: 2016
Author: Jianye Wang, Rui Ma
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 4 : pp. 517–535
Abstract
This paper is devoted to a unified a priori and a posteriori error analysis of CIP-FEM (continuous interior penalty finite element method) for second-order elliptic problems. Compared with the classic a priori error analysis in literature, our technique can easily apply for any type regularity assumption on the exact solution, especially for the case of lower $H^{1+s}$ weak regularity under consideration, where 0 ≤$s$≤ 1/2. Because of the penalty term used in the CIP-FEM, Galerkin orthogonality is lost and Céa Lemma for conforming finite element methods can not be applied immediately when 0≤$s$≤1/2. To overcome this difficulty, our main idea is introducing an auxiliary $C^1$ finite element space in the analysis of the penalty term. The same tool is also utilized in the explicit a posteriori error analysis of CIP-FEM.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2014.m834
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 4 : pp. 517–535
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Finite element methods continuous interior penalty priori error estimate posteriori error analysis.