Finite volumes and p-laplace operator
Title :
Finite volume schemes for nonlinear diffusion problems
Abstract :
Elliptic and parabolic PDEs involving nonlinear diffusion operators (of which the p-laplacian is a typical representative) can be successfully discretized by different kinds of numerical schemes.
We will look at finite volume discretizations that preserve some of the mathematical properties of the problem (coercivity, monotonicity, the variational structure, entropy and renormalized formulations).
Several schemes can be applied to the p-laplacian and p(x)-laplacian problems (complementary volumes schemes, schemes on cartesian meshes, DDFV schemes).
We will pay a particular attention to discrete duality formulas and other tools of discrete functional analysis for these schemes, and describe their use in the convergence proofs.
Boris ANDREIANOV
Laboratoire de Mathématiques - Université de Franche-Comté - Besançon
