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A Primal-Dual Weak Galerkin Finite Element Method for Fokker--Planck Type Equations
SIAM Journal on Numerical Analysis ( IF 2.9 ) Pub Date : 2020-01-01 , DOI: 10.1137/17m1126618
Chunmei Wang , Junping Wang

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.

中文翻译:

Fokker--Planck型方程的原始对偶弱Galerkin有限元方法

本文提出了一类Fokker-Planck型二阶椭圆方程的原始-对偶弱伽辽金(PD-WG)有限元方法。该方法基于变分形式,其中所有导数都应用于测试函数,因此模型方程的精确解不需要正则性。数值方案是通过使用局部构造的弱二阶偏导数和弱伽辽金上下文中常用的弱梯度设计的。为得到的数值解导出最佳收敛顺序。报告了数值结果以证明数值方案的性能。
更新日期:2020-01-01
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