Volume 8, Issue 5
Coefficient Jump-Independent Approximation of the Conforming and Nonconforming Finite Element Solutions

Shangyou Zhang

10.4208/aamm.2015.m931

Adv. Appl. Math. Mech., 8 (2016), pp. 722-736.

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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.

  • History

Published online: 2018-05

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