论文标题
针对具有低常规溶液的Div-Curl系统的原始双重弱彩色方法
A Primal-Dual Weak Galerkin Method for Div-Curl Systems with low-regularity solutions
论文作者
论文摘要
本文为DIV-CURL系统提供了一种新的原始双重弱彩素元素方法，该方法具有切向边界条件和溶液上的低规范性假设。该数值方案基于弱变异形式，涉及在弱的galerkin有限元方法的一般环境中，在一般环境中补充了双重或a关问题的精确溶液的部分衍生物。 $ h^θ（ω），\θ> \ frac12 $中的解决方案向量字段建立了$ l^2 $中的最佳订单错误估计。数学理论衍生在具有一般拓扑特性的连接域（即任意的第一和第二Betti数字）。据报道，数值结果以确认理论收敛。
This article presents a new primal-dual weak Galerkin finite element method for the div-curl system with tangential boundary conditions and low-regularity assumptions on the solution. The numerical scheme is based on a weak variational form involving no partial derivatives of the exact solution supplemented by a dual or ajoint problem in the general context of the weak Galerkin finite element method. Optimal order error estimates in $L^2$ are established for solution vector fields in $H^θ(Ω),\ θ>\frac12$. The mathematical theory was derived on connected domains with general topological properties (namely, arbitrary first and second Betti numbers). Numerical results are reported to confirm the theoretical convergence.
