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

Dan Li, Chunmei Wang

2023Numerical Methods for Partial Differential Equations10 citationsDOI Open Access PDF

Abstract

Abstract A 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.

Topics & Concepts

MathematicsFokker–Planck equationFinite element methodGalerkin methodDiscontinuous Galerkin methodNorm (philosophy)Applied mathematicsMathematical analysisType (biology)Partial differential equationPhysicsLawEcologyBiologyThermodynamicsPolitical scienceAdvanced Numerical Methods in Computational MathematicsDifferential Equations and Numerical MethodsNumerical methods for differential equations