Finite volume schemes for the p-Laplacian on Cartesian meshes

Boris Andreianov; Franck Boyer; Florence Hubert

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 38, Issue: 6, page 931-959
  • ISSN: 0764-583X

Abstract

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This paper is concerned with the finite volume approximation of the p-Laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh's interfaces is needed in order to discretize the p-Laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally conservative and in addition derive from the minimization of a strictly convexe and coercive discrete functional. The convergence rate is analyzed when the solution lies in W2,p. Numerical results are given in order to compare different admissible and non-admissible schemes.

How to cite

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Andreianov, Boris, Boyer, Franck, and Hubert, Florence. "Finite volume schemes for the p-Laplacian on Cartesian meshes." ESAIM: Mathematical Modelling and Numerical Analysis 38.6 (2010): 931-959. <http://eudml.org/doc/194250>.

@article{Andreianov2010,
abstract = { This paper is concerned with the finite volume approximation of the p-Laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh's interfaces is needed in order to discretize the p-Laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally conservative and in addition derive from the minimization of a strictly convexe and coercive discrete functional. The convergence rate is analyzed when the solution lies in W2,p. Numerical results are given in order to compare different admissible and non-admissible schemes. },
author = {Andreianov, Boris, Boyer, Franck, Hubert, Florence},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite volume methods; p-Laplacian; error estimates.; finite volume scheme; Cartesian meshes; numerical experiments},
language = {eng},
month = {3},
number = {6},
pages = {931-959},
publisher = {EDP Sciences},
title = {Finite volume schemes for the p-Laplacian on Cartesian meshes},
url = {http://eudml.org/doc/194250},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Andreianov, Boris
AU - Boyer, Franck
AU - Hubert, Florence
TI - Finite volume schemes for the p-Laplacian on Cartesian meshes
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 6
SP - 931
EP - 959
AB - This paper is concerned with the finite volume approximation of the p-Laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh's interfaces is needed in order to discretize the p-Laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally conservative and in addition derive from the minimization of a strictly convexe and coercive discrete functional. The convergence rate is analyzed when the solution lies in W2,p. Numerical results are given in order to compare different admissible and non-admissible schemes.
LA - eng
KW - Finite volume methods; p-Laplacian; error estimates.; finite volume scheme; Cartesian meshes; numerical experiments
UR - http://eudml.org/doc/194250
ER -

References

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