A Primal-Dual Weak Galerkin Finite Element Method for Fokker-Planck Type Equations
This work provides a new numerical method for solving Fokker-Planck type equations, which are important in fields like physics and finance, but the contribution is incremental as it extends existing weak Galerkin techniques.
The paper proposes a primal-dual weak Galerkin finite element method for Fokker-Planck type equations, achieving optimal order convergence without requiring regularity of the exact solution. Numerical results confirm the scheme's performance.
This paper presents a primal-dual weak Galerkin (PD-WG) finite element method for a class of second order elliptic equations of Fokker-Planck type. The method is based on a variational form where all the derivatives are applied to the test functions so that no regularity is necessary for the exact solution of the model equation. The numerical scheme is designed by using locally constructed weak second order partial derivatives and the weak gradient commonly used in the weak Galerkin context. Optimal order of convergence is derived for the resulting numerical solutions. Numerical results are reported to demonstrate the performance of the numerical scheme.