A simplified primal‐dual weak Galerkin finite element method for Fokker–Planck‐type equations

Abstract

AbstractA simplified primal‐dual weak Galerkin (S‐PDWG) finite element method is designed for the Fokker–Planck‐type equation with nonsmooth diffusion tensor and drift vector. The discrete system resulting from S‐PDWG method has significantly fewer degrees of freedom compared with the one resulting from the PDWG method proposed by Wang‐Wang. Furthermore, the condition number of the S‐PDWG method is smaller than the PDWG method (Wang‐Wang) due to the introduction of a new stabilizer, which provides a potential to design fast algorithms. Optimal‐order error estimates for the S‐PDWG approximation are established in the norm. A series of numerical results are demonstrated to validate the accuracy and efficiency of the S‐PDWG method.