Year: 2020
Author: Wei Pi, Hao Wang, Xiaoping Xie
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 1 : pp. 40–56
Abstract
A simple post-processing technique for finite element methods with $L$2-superconvergence is proposed. It provides more accurate approximations for solutions of two- and three-dimensional systems of partial differential equations. Approximate solutions can be constructed locally by using finite element approximations $u$$h$ provided that $u$$h$ is superconvergent for a locally defined projection $\widetilde{P}$$h$$u$. The construction is based on the least-squares fitting algorithm and local $L$2-projections. Error estimates are derived and numerical examples illustrate the effectiveness of this approach for finite element methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.170119.200519
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 1 : pp. 40–56
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Finite element method post-processing least-square fitting $L^2$-superconvergence.