Year: 2021
Author: Yanhui Zhou, Qingsong Zou
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 1 : pp. 19–37
Abstract
In this paper, we post-process an eight-node-serendipity finite element solution for elliptic equations. In the post-processing procedure, we first construct a $control$ $volume$ for each node in the serendipity finite element mesh, then we enlarge the serendipity finite element space by adding some appropriate element-wise bubbles and require the novel solution to satisfy the local conservation law on each control volume. Our post-processing procedure can be implemented in a parallel computing environment and its computational cost is proportional to the cardinality of the serendipity elements. Moreover, both our theoretical analysis and numerical examples show that the postprocessed solution converges to the exact solution with optimal convergence rates both under $H^1$ and $L^2$ norms. A numerical experiment for a single-phase porous media problem validates the necessity of the post-processing procedure.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2021-IJNAM-18619
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 1 : pp. 19–37
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Postprocessing serendipity finite elements local conservation laws error estimates.