Volume 10, Issue 1
A New Post-Processing Technique for Finite Element Methods with $L^2$-Superconvergence

East Asian J. Appl. Math., 10 (2020), pp. 40-56.

Published online: 2020-01

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• 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.

65N30, 65N15

512442593@qq.com (Wei Pi)

wangh@scu.edu.cn (Hao Wang)

xpxie@scu.edu.cn (Xiaoping Xie)

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@Article{EAJAM-10-40, author = {Pi , WeiWang , Hao and Xie , Xiaoping}, title = {A New Post-Processing Technique for Finite Element Methods with $L^2$-Superconvergence}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {1}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.170119.200519}, url = {http://global-sci.org/intro/article_detail/eajam/13577.html} }
TY - JOUR T1 - A New Post-Processing Technique for Finite Element Methods with $L^2$-Superconvergence AU - Pi , Wei AU - Wang , Hao AU - Xie , Xiaoping JO - East Asian Journal on Applied Mathematics VL - 1 SP - 40 EP - 56 PY - 2020 DA - 2020/01 SN - 10 DO - http://doi.org/10.4208/eajam.170119.200519 UR - https://global-sci.org/intro/article_detail/eajam/13577.html KW - Finite element method, post-processing, least-square fitting, $L^2$-superconvergence. AB -

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.

WeiPi, HaoWang & XiaopingXie. (2020). A New Post-Processing Technique for Finite Element Methods with $L^2$-Superconvergence. East Asian Journal on Applied Mathematics. 10 (1). 40-56. doi:10.4208/eajam.170119.200519
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