@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} }