Finite volume schemes for the p-Laplacian on Cartesian meshes
Département de Mathématiques, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France.
2 Laboratoire d'Analyse, Topologie et Probabilités, 39 rue F. Joliot Curie, 13453 Marseille Cedex 13, France. firstname.lastname@example.org.
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.
Mathematics Subject Classification: 35J65 / 65N15 / 74S10
Key words: Finite volume methods / p-Laplacian / error estimates.
© EDP Sciences, SMAI, 2004