# 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 (2011)

- Volume: 45, Issue: 4, page 627-650
- ISSN: 0764-583X

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topOmnes, 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 45.4 (2011): 627-650. <http://eudml.org/doc/197523>.

@article{Omnes2011,

abstract = {
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).
},

author = {Omnes, Pascal},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Finite volume method; Laplace equation; Delaunay meshes; Voronoi meshes; convergence; error estimates; finite volume method},

language = {eng},

month = {1},

number = {4},

pages = {627-650},

publisher = {EDP Sciences},

title = {On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes},

url = {http://eudml.org/doc/197523},

volume = {45},

year = {2011},

}

TY - JOUR

AU - Omnes, Pascal

TI - On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2011/1//

PB - EDP Sciences

VL - 45

IS - 4

SP - 627

EP - 650

AB -
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).

LA - eng

KW - Finite volume method; Laplace equation; Delaunay meshes; Voronoi meshes; convergence; error estimates; finite volume method

UR - http://eudml.org/doc/197523

ER -

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