Name
Title | ||
|---|---|---|
A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure. |
Abstract | ||
|---|---|---|
We propose a finite volume scheme for a class of nonlinear parabolic equations endowed with non-homogeneous Dirichlet boundary conditions and which admit relative entropy functionals. For this kind of models including porous media equations, Fokker–Planck equations for plasma physics or dumbbell models for polymer flows, it has been proved that the transient solution converges to a steady-state when time goes to infinity. The present scheme is built from a discretization of the steady equation and preserves steady-states and natural Lyapunov functionals which provide a satisfying long-time behavior. After proving well-posedness, stability, exponential return to equilibrium and convergence, we present several numerical results which confirm the accuracy and underline the efficiency to preserve large-time asymptotic. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s00211-017-0885-7 | Numerische Mathematik |
Keywords | Field | DocType |
65M08, 65M12, 76S05, 76X05, 82D60 | Convection–diffusion equation,Dumbbell,Mathematical optimization,Mathematical analysis,Dirichlet boundary condition,Infinity,Plasma,Porous medium,Finite volume method,Kullback–Leibler divergence,Mathematics | Journal |
Volume | Issue | ISSN |
137 | 3 | 0029-599X |
Citations | PageRank | References |
3 | 0.51 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Francis Filbet | 1 | 271 | 37.95 |
| Maxime Herda | 2 | 3 | 0.51 |