East Asian J. Appl. Math., 10 (2020), pp. 40-56.
Published online: 2020-01
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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} }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.