A New Post-Processing Technique for Finite Element Methods with $L^2$-Superconvergence

A New Post-Processing Technique for Finite Element Methods with $L^2$-Superconvergence

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.

Author Details

Wei Pi

Hao Wang

Xiaoping Xie