Large time behavior of nonlinear finite volume schemes for convection-diffusion equations
Abstract
In this contribution we analyze the large time behavior of a family of nonlinear finite volume schemes for anisotropic convection-diffusion equations set in a bounded bidimensional domain and endowed with either Dirichlet and / or no-flux boundary conditions. We show that solutions to the two-point flux approximation (TPFA) and discrete duality finite volume (DDFV) schemes under consideration converge exponentially fast toward their steady state. The analysis relies on discrete entropy estimates and discrete functional inequalities. As a biproduct of our analysis, we establish new discrete Poincar\'e-Wirtinger, Beckner and logarithmic Sobolev inequalities. Our theoretical results are illustrated by numerical simulations.
Keywords
Cite
@article{arxiv.1911.04962,
title = {Large time behavior of nonlinear finite volume schemes for convection-diffusion equations},
author = {Clément Cancès and Claire Chainais-Hillairet and Maxime Herda and Stella Krell},
journal= {arXiv preprint arXiv:1911.04962},
year = {2020}
}
Comments
version accepted in SINUM