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A discrete duality finite volume approach to Hodge decomposition and div-curl problems on almost arbitrary two-dimensional meshes

Abstract : We define discrete differential operators such as grad, div and curl, on general two-dimensional meshes. These operators verify discrete analogues of usual continuous theorems Green formulae, Hodge decomposition of vector fields, 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 and present numerical results on several types of meshes,among which degenerating meshes and non-conforming meshes.
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Submitted on : Thursday, October 31, 2019 - 4:23:19 PM
Last modification on : Tuesday, April 28, 2020 - 11:28:13 AM

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S. Delcourte, K. Domelevo, P. Omnes. A discrete duality finite volume approach to Hodge decomposition and div-curl problems on almost arbitrary two-dimensional meshes. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2007, 45, ⟨10.1137/060655031⟩. ⟨cea-02341906⟩

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