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A positive scheme for diffusion problems on deformed meshes
Author(s) -
Blanc Xavier,
Labourasse Emmanuel
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201400234
Subject(s) - polygon mesh , transpose , convergence (economics) , computation , scheme (mathematics) , nonlinear system , mathematics , matrix (chemical analysis) , domain decomposition methods , domain (mathematical analysis) , finite volume method , positive definite matrix , point (geometry) , computer science , mathematical optimization , algorithm , finite element method , mathematical analysis , geometry , physics , eigenvalues and eigenvectors , materials science , quantum mechanics , mechanics , economics , composite material , thermodynamics , economic growth
We present in this article a positive finite volume method for diffusion equation on deformed meshes. This method is mainly inspired from [50][Z. Sheng, 2009], [52][S. Wang, 2012], and uses auxiliary unknowns at the nodes of the mesh. The flux is computed so as to be a two‐point nonlinear flux, giving rise to a matrix which is the transpose of an M‐matrix, which ensures that the scheme is positive. A particular attention is given to the computation of the auxiliary unknowns. We propose a new strategy, which aims at providing a scheme easy to implement in a parallel domain decomposition setting. An analysis of the scheme is provided: existence of a solution for the nonlinear system is proved, and the convergence of a fixed‐point strategy is studied.