A simplified primal-dual weak Galerkin finite element method for Fokker-Planck type equations
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A simplified primal-dual weak Galerkin (S-PDWG) finite element method is designed for the Fokker-Planck type equation with non-smooth 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 <cit.>. Furthermore, the condition number of the S-PDWG method is smaller than the PDWG method <cit.> due to the introduction of a new stabilizer, which provides a potential for designing fast algorithms. Optimal order error estimates for the S-PDWG approximation are established in the L^2 norm. A series of numerical results are demonstrated to validate the effectiveness of the S-PDWG method.
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