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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:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation