01-17
On the superconvergence of nonconforming low order finite elementsapplied to the Poisson equation
by Lin, Qun; Tobiska, Lutz; Zhou, Aihui
Preprint series: 01-17, Preprints
- MSC:
- 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
- 65N12 Stability and convergence of numerical methods
- 65N15 Error bounds
Abstract: It is well-known that on uniform meshes the piecewise linear, conforming finite element solution of Poisson equation approximates the interpolant of higher order than the solution itselfs. In this paper, this type of superclose property is studied for nonconforming finite element of lowest order. By giving explicite examples we show that some nonconforming finite elements do not admit the superclose property. In particular, we discuss two nonconforming finite elements which satisfy the superclose property. Moreover, applying a postprocessing technique, we can also state a superconvergence property for the error of the postprocessed discrete solution to the solution itself.
Keywords: Nonconforming finite elements, superconvergence, postprocessing
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