Large time behavior of nonlinear finite volume schemes for convection-diffusion equations
SIAM JOURNAL ON NUMERICAL ANALYSIS(2020)
摘要
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 Poincare-Wirtinger, Beckner, and logarithmic Sobolev inequalities. Our theoretical results are illustrated by numerical simulations.
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关键词
finite volume methods,long-time behavior,entropy methods,discrete functional inequalities,logarithmic Sobolev inequalities
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