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2001-17

On the superconvergence of nonconfor

by Lin, Qun, Tobiska, Lutz, Zhou, Aihui.


Series: 2001-17, 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 fin