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Volume 17, Issue 5
Locally Conservative Finite Element Solutions for Parabolic Equations

Wenbo Gong & Qingsong Zou

Int. J. Numer. Anal. Mod., 17 (2020), pp. 679-694.

Published online: 2020-08

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  • Abstract

In this paper, we post-process the finite element solutions for parabolic equations to meet discrete conservation laws in element-level. The post-processing procedure are implemented by two different approaches: one is by computing a globally continuous flux function and the other is by computing the so-called finite-volume-element-like solution. Both approaches only require to solve a small linear system on each element of the underlying mesh. The post-processed flux converges to the exact flux with optimal convergence rates. Numerical computations verify our theoretical findings.

  • Keywords

Conservation laws, postprocessing, finite volume solution.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-17-679, author = {Gong , Wenbo and Zou , Qingsong}, title = {Locally Conservative Finite Element Solutions for Parabolic Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {5}, pages = {679--694}, abstract = {

In this paper, we post-process the finite element solutions for parabolic equations to meet discrete conservation laws in element-level. The post-processing procedure are implemented by two different approaches: one is by computing a globally continuous flux function and the other is by computing the so-called finite-volume-element-like solution. Both approaches only require to solve a small linear system on each element of the underlying mesh. The post-processed flux converges to the exact flux with optimal convergence rates. Numerical computations verify our theoretical findings.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/17876.html} }
TY - JOUR T1 - Locally Conservative Finite Element Solutions for Parabolic Equations AU - Gong , Wenbo AU - Zou , Qingsong JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 679 EP - 694 PY - 2020 DA - 2020/08 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/17876.html KW - Conservation laws, postprocessing, finite volume solution. AB -

In this paper, we post-process the finite element solutions for parabolic equations to meet discrete conservation laws in element-level. The post-processing procedure are implemented by two different approaches: one is by computing a globally continuous flux function and the other is by computing the so-called finite-volume-element-like solution. Both approaches only require to solve a small linear system on each element of the underlying mesh. The post-processed flux converges to the exact flux with optimal convergence rates. Numerical computations verify our theoretical findings.

Wenbo Gong & Qingsong Zou. (2020). Locally Conservative Finite Element Solutions for Parabolic Equations. International Journal of Numerical Analysis and Modeling. 17 (5). 679-694. doi:
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