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Discrete maximum principle based on repair technique for diamond type scheme of diffusion problems
Author(s) -
Wang Shuai,
Yuan Guangwei,
Li Yonghai,
Sheng Zhiqiang
Publication year - 2012
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2746
Subject(s) - polygon mesh , finite element method , conservation law , diamond , mathematics , diffusion , scheme (mathematics) , computer science , mathematical optimization , topology (electrical circuits) , mathematical analysis , engineering , physics , geometry , materials science , structural engineering , composite material , thermodynamics , combinatorics
SUMMARY In this paper, two repair techniques are proposed for diamond schemes of anisotropic diffusion problems to ensure that the repaired solutions satisfy the discrete maximum principle. One of them is an extension of that in [Liska R, Shashkov M. Enforcing the discrete maximum principle for linear finite element solutions of second‐order elliptic problems. Communications in Computational Physics 2008; 3(4):852–877.] for linear finite element solutions, which is a local repair technique, and another is a new global repair technique. Both of them keep total energy conservation and are easy to be implemented in existing codes. Numerical examples show that these two repair techniques do not destroy the accuracy of solution for the diamond schemes on distorted meshes. Copyright © 2012 John Wiley & Sons, Ltd.