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.