On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 4, pp. 627-650.

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).

DOI : 10.1051/m2an/2010068
Classification : 65N15, 65N30, 35J05
Mots-clés : finite volume method, Laplace equation, Delaunay meshes, Voronoi meshes, convergence, error estimates 
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     title = {On the second-order convergence of a function reconstructed from finite volume approximations of the {Laplace} equation on {Delaunay-Voronoi} meshes},
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Omnes, Pascal. On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 4, pp. 627-650. doi : 10.1051/m2an/2010068. http://www.numdam.org/articles/10.1051/m2an/2010068/

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