Paper Info
Title
The finite volume scheme preserving maximum principle for diffusion equations with discontinuous coefficient
Abstract
We construct a new scheme whose primary unknowns include both cell-centered unknowns and edge unknowns on discontinuous line to solve diffusion equations with discontinuous coefficient. First, two linear fluxes are given on both sides of the cell edge, respectively. In order to deal with the defect of the existing scheme preserving maximum principle for solving diffusion problem with discontinuous coefficient, in addition to cell-centered unknowns, we also introduce cell-edge unknowns on discontinuous line as basic unknowns. Second, the conservative flux is constructed by using nonlinear weighted combination of these two linear fluxes. For the cell-edge unknowns on discontinuous line, we add an equation by using the continuity of normal flux. Compared to the classical cell-centered nonlinear finite volume scheme, the introduction of cell-edge unknowns on discontinuous edge is the key point for our scheme to solve diffusion equations with discontinuous coefficient. Then we prove that the scheme satisfies the discrete maximum principle. Based on this, the existence of a solution for the scheme is also obtained. Numerical results are presented to show that our scheme obtains almost second order accuracy for solution on random meshes, preserves discrete maximum principle, and is superior to the existing scheme (in Sheng and Yuan (2011)) preserving the maximum principle on dealing with the problems with strong anisotropic discontinuous coefficient on distorted meshes.
Year
DOI
Venue
2020
10.1016/j.camwa.2019.10.012
Computers & Mathematics with Applications
Keywords
DocType
Volume
Maximum principle,Finite volume scheme,Diffusion equation,Discontinuous coefficient
Journal
79
Issue
ISSN
Citations 
8
0898-1221
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Yao Yu15814.13
Guangwei Yuan216523.06
Zhiqiang Sheng312914.39
Yonghai Li400.34