Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation
Authors: Qun Lin1; Lutz Tobiska2; Aihui Zhou3
Source: IMA Journal of Numerical Analysis, Volume 25, Number 1, 01 January 2005 , pp. 160-181(22)
Publisher: Oxford University Press
- Free Content
- New Content
- Subscribed Content
- Free Trial Content
Abstract:
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.Keywords: non-conforming finite elements; superconvergence; postprocessing; extrapolation
Document Type: Research article
DOI: 10.1093/imanum/drh008
Affiliations: 1: Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, PO Box 2719, Beijing, 100080, China, 2: Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, PSF 4120, D-39016 Magdeburg, Germany, 3: Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, PO Box 2719, Beijing, 100080, China
- Free Content
- New Content
- Subscribed Content
- Free Trial Content
Click here for Page Help