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 - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 4, p. 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 : https://doi.org/10.1051/m2an/2010068
Classification:  65N15,  65N30,  35J05
Keywords: finite volume method, Laplace equation, Delaunay meshes, Voronoi meshes, convergence, error estimates
@article{M2AN_2011__45_4_627_0,
     author = {Omnes, Pascal},
     title = {On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {4},
     year = {2011},
     pages = {627-650},
     doi = {10.1051/m2an/2010068},
     zbl = {1269.65109},
     mrnumber = {2804653},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2011__45_4_627_0}
}
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 - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 4, pp. 627-650. doi : 10.1051/m2an/2010068. http://www.numdam.org/item/M2AN_2011__45_4_627_0/

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