Structure preserving schemes for Fokker-Planck equations of irreversible processes. (English) Zbl 1530.65087
Summary: In this paper, we construct structure preserving schemes for solving Fokker-Planck equations associated with irreversible processes. The proposed method is first order in time. We consider two structure-preserving spatial discretizations, which are second order and fourth order accurate finite difference schemes. They are derived via finite difference implementation of the classical \(Q^k\) (\(k=1,2\)) finite element methods on uniform meshes. Under mild mesh conditions and practical time step constraints, the schemes are proved monotone, thus are positivity-preserving and energy dissipative. In particular, our scheme is suitable for capturing steady state solutions in large final time simulations.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35Q84 | Fokker-Planck equations |
Keywords:
Fokker-Planck equation; finite difference; monotonicity; positivity; energy dissipation; high-order accuracyReferences:
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