A positive scheme for diffusion problems on deformed meshes

作者：Blanc Xavier^*; Labourasse Emmanuel

来源：ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 2016, 96(6): 660-680.

DOI：10.1002/zamm.201400234

• Deformed mesh
• finite volume
• diffusion
• maximum principle
• numerical analysis

We present in this article a positive finite volume method for diffusion equation on deformed meshes. This method is mainly inspired from [50, 52], 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.

• 出版日期2016-6
• 单位中国地震局