Volume 45, Number 4, July-August 2011
|Page(s)||627 - 650|
|Published online||30 November 2010|
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.