论文标题
fokker-Planck类型方程的简化原始双重弱型galerkin有限元法
A simplified primal-dual weak Galerkin finite element method for Fokker-Planck type equations
论文作者
论文摘要
一种简化的原始双重弱甘油素（S-PDWG）有限元方法是为具有非平滑扩散张量和漂移矢量的Fokker-Planck类型方程设计的。与Wang-Wang \ cite {WW-FP-2018}提出的PDWG方法相比，由S-PDWG方法产生的离散系统具有较少的自由度。此外，由于引入了新的稳定器，S-PDWG方法的条件数小于PDWG方法\ cite {WW-FP-2018}，该新稳定器为设计快速算法提供了潜力。 S-PDWG近似的最佳订单错误估计是在$ l^2 $ norm中建立的。证明了一系列数值结果可以验证S-PDWG方法的有效性。
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 \cite{WW-fp-2018}. Furthermore, the condition number of the S-PDWG method is smaller than the PDWG method \cite{WW-fp-2018} 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.
