On the Second-order Convergence of Finite Volume Methods for the Laplace Equation on Delaunay-voronoi Meshes
نویسنده
چکیده
Abstract. Cell-centered and vertex-centered finite volume schemes for the Laplace equation with homogeneous Dirichlet boundary conditions are considered on triangular meshes and their Voronoi duals. On a two-dimensional convex polygonal domain, it is shown that a suitable combination of the solutions of these two schemes converges with second-order accuracy towards the exact solution in the L norm, under the sufficient condition that the right-hand side of the Laplace equation belongs to H(Ω).
منابع مشابه
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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