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 - <p style="text-align: justify;">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.</p>