Coefficient Jump-Independent Approximation of the Conforming and Nonconforming Finite Element Solutions

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.

Author Details

Shangyou Zhang