A New Numerical Method for Div-Curl Systems with Low Regularity Assumptions
A New Numerical Method for Div-Curl Systems with Low Regularity Assumptions
复制标题
DOI：
10.1016/j.camwa.2022.03.015
复制
发表时间：
2021-01
期刊：
影响因子：
--
通讯作者：
Shuhao Cao;Chunmei Wang;Junping Wang
中科院分区：
文献类型：
--
作者：
Shuhao Cao;Chunmei Wang;Junping Wang
本文利用原对偶弱伽辽金（PDWG）有限元方法，对具有法向边界条件的div-curl方程组提出了一种新的数值方法。div-curl系统的PDWG有限元格式有两个突出的特点，即它不仅在低H α正则性（α> 0）假设下提供了div-curl系统的精确可靠的数值解，而且在具有复杂拓扑结构的区域上提供了法向调和向量场的有效逼近.七个数值实验的结果表明，PDWG算法的性能，包括一个例子的离散法向谐波矢量场的计算。
This paper presents a new numerical method for div-curl systems with the normal boundary condition by using a finite element technique known as primal-dual weak Galerkin (PDWG). The PDWG finite element scheme for the div-curl system has two prominent features in that it offers not only an accurate and reliable numerical solution to the div-curl system under the low H α-regularity (α> 0) assumption for the true solution, but also an effective approximation of the normal harmonic vector fields on domains with complex topology. Seven numerical experiments are conducted and the results are presented to demonstrate the performance of the PDWG algorithm, including one example on the computation of discrete normal harmonic vector fields.