Nonlinear free energy diminishing schemes for convection-diffusion equations: convergence and long time behaviour
De
Claire Chainais-Hillairet
Apparaît dans la collection : POEMs - POlytopal Element Methods in Mathematics and Engineering
The aim of the talk is to introduce a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift-diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation relation. This relation is of paramount importance to capture the long-time behavior of the problem in an accurate way. To enforce it, the linear convection diffusion equation is rewritten in a nonlinear form before being discretized. This is a joint work with Clément Cancès (Lille) and Stella Krell (Nice).
