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 - <p style="text-align: justify;">A simple post-processing technique for finite element methods with $L$<sup>2</sup>-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 $u$<sub>$h$</sub> provided that <span style="text-align: justify;">$u$</span><sub style="text-align: justify; white-space: normal;">$h$</sub> is superconvergent for a locally defined projection $\widetilde{P}$<sub>$h$</sub>$u$. The construction is based on the least-squares fitting algorithm and local $L$<sup>2</sup>-projections. Error estimates are derived and numerical examples illustrate the effectiveness of this approach for finite element methods.</p>