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.