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An anisotropic nonconforming finite element with some superconvergence results. (English) Zbl 1074.65133

The authors first study the anisotropic interpolation property of a nonconforming finite element proposed by H. Han [J. Comput. Math. 2, 223–233 (1984; Zbl 0573.65083)] and visualizing its important role in estimating the interpolation error, they obtain the consistency error estimate. Superclose property and superconvergence estimates on the centres of the elements are also obtained without the regularity assumption and quasi-uniform assumption requirements on the meshes. Some numerical examples are presented to illustrate the validity of the theoretical analysis.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Citations:

Zbl 0573.65083
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