A primal-dual finite element method for first-order transport problems
A primal-dual finite element method for first-order transport problems
复制标题
DOI：
10.1016/j.jcp.2020.109571
复制
发表时间：
2019-06
期刊：
影响因子：
--
通讯作者：
Chunmei Wang;Junping Wang
中科院分区：
文献类型：
--
作者：
Chunmei Wang;Junping Wang
利用科学计算中新近发展起来的原始-对偶弱伽辽金（PD-WG）有限元方法，设计了一种求解一阶输运问题的新的数值方法。的PD-WG方法是基于变分制定的建模方程的微分算子应用于测试功能，使低正则性的精确解的原始方程是足够的计算。PD-WG有限元法确实产生了一个对称系统，涉及原始变量的原始方程和对偶变量的对偶方程（也称为拉格朗日乘子）。对于线性运输问题，它示出的PD-WG方法提供的数值解，保持质量局部每个元素。在各种规范的最优阶误差估计来自PD-WG方法与弱正则性假设的建模方程的数值解。各种数值结果证明了新方法的准确性和稳定性。
This article devises a new numerical method for first-order transport problems by using the primal-dual weak Galerkin (PD-WG) finite element method recently developed in scientific computing. The PD-WG method is based on a variational formulation of the modeling equation for which the differential operator is applied to the test function so that low regularity for the exact solution of the original equation is sufficient for computation. The PD-WG finite element method indeed yields a symmetric system involving both the original equation for the primal variable and its dual for the dual variable (also known as Lagrangian multiplier). For the linear transport problem, it is shown that the PD-WG method offers numerical solutions that conserve mass locally on each element. Optimal order error estimates in various norms are derived for the numerical solutions arising from the PD-WG method with weak regularity assumptions on the modelling equations. A variety of numerical results are presented to demonstrate the accuracy and stability of the new method.