论文标题
$ l^p $ - div-curl系统的原始双二重弱彩手方法
An $L^p$- Primal-Dual Weak Galerkin method for div-curl Systems
论文作者
论文摘要
本文提出了一种新的$ l^p $ - 主要双弱的弱彩手（PDWG），用于Div-Curl系统的有限元方法，其正常边界条件为$ p> 1 $。建议的$ l^p $ -pdwg有限元方案的两个关键功能如下：（1）在低$ w^{α，p} $ - 正常度（$α> 0 $）的基本解决方案的假设下，它为Div-Curl系统提供了准确且可靠的数值解决方案； （2）它在具有复杂拓扑的域上提供了正常谐波矢量场的有效近似值。对于原始变量的$ l^q $ -norm中，建立了最佳订单误差估计，其中$ \ frac {1} {p} {p}+\ frac {1} {q} = 1 $。提出了一系列数值实验，以证明所提出的$ l^p $ -PDWG算法的性能。
This paper presents a new $L^p$-primal-dual weak Galerkin (PDWG) finite element method for the div-curl system with the normal boundary condition for $p>1$. Two crucial features for the proposed $L^p$-PDWG finite element scheme are as follows: (1) it offers an accurate and reliable numerical solution to the div-curl system under the low $W^{α, p}$-regularity ($α>0$) assumption for the exact solution; (2) it offers an effective approximation of the normal harmonic vector fields on domains with complex topology. An optimal order error estimate is established in the $L^q$-norm for the primal variable where $\frac{1}{p}+\frac{1}{q}=1$. A series of numerical experiments are presented to demonstrate the performance of the proposed $L^p$-PDWG algorithm.
