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

Part of: Partial differential equations, boundary value problems Numerical approximation and computational geometry

Published online by Cambridge University Press:  08 July 2016

Shangyou Zhang
Shangyou Zhang*
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
*
*Corresponding author. Email:szhang@udel.edu (S. Y. Zhang)
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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 L2-projection, and in solving elliptic differential equation, independent of the coefficient jump in the elliptic differential equation. Numerical tests confirm the theoretical finding.

Keywords

Jump coefficientfinite elementL2 projectionweighted projectionScott-Zhang operator

MSC classification

Secondary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65D05: Interpolation
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 5 , October 2016 , pp. 722 - 736
Copyright
Copyright © Global-Science Press 2016 

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