NDLI: A Discrete Duality Finite Volume Approach to Hodge Decomposition and divcurl Problems on Almost Arbitrary TwoDimensional Meshes

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Delcourte, Sarah Domelevo, Komla Omnes, Pascal
Copyright Year	2007
Abstract	We define discrete differential operators such as gradient, divergence, and curl, on general twodimensional 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 divcurl 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.
Starting Page	1142
Ending Page	1174
Page Count	33
File Format	PDF
ISSN	00361429
DOI	10.1137/060655031
e-ISSN	10957170
Issue Number	3
Volume Number	45
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2007-05-10
Access Restriction	Subscribed
Subject Keyword	discrete Green formula discrete differential operators convergence discrete duality finite volume method Stability and convergence of numerical methods PDEs in connection with optics and electromagnetic theory divcurl equations discrete Hodge decomposition arbitrary meshes degenerating meshes Error bounds nonconforming meshes Electro- and magnetostatics Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods error estimates
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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