Paper Info
Title
Monotone Finite Volume Schemes for Diffusion Equation with Imperfect Interface on Distorted Meshes.
Abstract
In this paper, we prove the solution of diffusion equation with imperfect interface is positivity-preserving and a monotone finite volume method is presented to obtain the nonnegative solution on distorted mesh. Motivated by Sheng and Yuan (J Comput Phys 231:3739–3754, 2012), the discrete normal flux on interface is defined by using an extended stencil and introducing two auxiliary points to distinguish the discontinuities of the unknowns on both sides of the interface. The resulting finite volume scheme is locally conservative and has only cell-centered unknowns. Moreover, it is proved to be monotone. The numerical results show that the method obtains second order convergent rate in \(L_2\) norms for solutions on quadrilateral and triangular meshes.
Year
DOI
Venue
2018
10.1007/s10915-018-0651-8
J. Sci. Comput.
Keywords
Field
DocType
Monotone, Finite volume scheme, Elliptic interface problem, Distorted mesh, Jump condition
Classification of discontinuities,Polygon mesh,Imperfect,Mathematical analysis,Stencil,Quadrilateral,Finite volume method,Mathematics,Monotone polygon,Diffusion equation
Journal
Volume
Issue
ISSN
76
2
0885-7474
Citations 
PageRank 
References 
0
0.34
15
Authors
3
Name
Order
Citations
PageRank
Fujun Cao100.34
Zhiqiang Sheng212914.39
Guangwei Yuan316523.06