On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes
CEA, DEN, DM2S-SFME, 91191 Gif-sur-Yvette Cedex, France.
2 Université Paris 13, LAGA, CNRS UMR 7539, Institut Galilée, 99 avenue J.-B. Clément, 93430 Villetaneuse Cedex, France.
Revised: 30 July 2010
Cell-centered and vertex-centered finite volume schemes for the Laplace equation with homogeneous Dirichlet boundary conditions are considered on a triangular mesh and on the Voronoi diagram associated to its vertices. A broken P1 function is constructed from the solutions of both schemes. When the domain is two-dimensional polygonal convex, it is shown that this reconstruction converges with second-order accuracy towards the exact solution in the L2 norm, under the sufficient condition that the right-hand side of the Laplace equation belongs to H1(Ω).
Mathematics Subject Classification: 65N15 / 65N30 / 35J05
Key words: Finite volume method / Laplace equation / Delaunay meshes / Voronoi meshes / convergence / error estimates
© EDP Sciences, SMAI, 2010