Coefficient Jump-Independent Approximation of the Conforming and Nonconforming Finite Element Solutions
Year: 2016
Author: Shangyou Zhang
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 5 : pp. 722–736
Abstract
A counterexample is constructed. It confirms that the error of conforming finite element solution is proportional to the coefficient jump, when solving interface elliptic equations. The Scott-Zhang operator is applied to a nonconforming finite element. It is shown that the nonconforming finite element provides the optimal order approximation in interpolation, in $L^2$-projection, and in solving elliptic differential equation, independent of the coefficient jump in the elliptic differential equation. Numerical tests confirm the theoretical finding.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2015.m931
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 5 : pp. 722–736
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Jump coefficient finite element $L^2$ projection weighted projection Scott-Zhang operator.