期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 45, 期 3, 页码 1142-1174出版社
SIAM PUBLICATIONS
DOI: 10.1137/060655031
关键词
discrete duality finite volume method; discrete Green formula; discrete Hodge decomposition; discrete differential operators; div-curl equations; arbitrary meshes; nonconforming meshes; degenerating meshes; convergence; error estimates
We de. ne discrete differential operators such as gradient, divergence, and curl, on general two-dimensional nonorthogonal meshes. These discrete operators verify discrete analogues of usual continuous theorems: discrete Green formulae, discrete Hodge decomposition of vector fields, and vector curls have a vanishing divergence and gradients have a vanishing curl. We apply these ideas to discretize div-curl systems. We give error estimates based on the reformulation of these systems into equivalent equations for the potentials. Numerical results illustrate the use of the method on several types of meshes, some of which are degenerating triangular meshes and nonconforming locally refined meshes.
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