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Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation
Ist Teil von
IMA journal of numerical analysis, 2005-01, Vol.25 (1), p.160-181
Ort / Verlag
Oxford: Oxford University Press
Erscheinungsjahr
2005
Link zum Volltext
Quelle
Oxford University Press Journals Current
Beschreibungen/Notizen
It is well-known that on uniform meshes the piecewise linear conforming finite element solution of the Poisson equation approximates the interpolant to a higher order than the solution itself. In this paper, this type of superclose property is studied for the canonical interpolant defined by the nodal functionals of several non-conforming finite elements of lowest order. By giving explicit examples we show that some non-conforming finite elements do not admit the superclose property. In particular, we discuss two non-conforming finite elements which satisfy the superclose property. Moreover, applying a postprocessing technique, we can also state a superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself. Finally, we show that an extrapolation technique leads to a further improvement of the accuracy of the finite element solution.