This paper presents a numerical method for div-curl systems with normal boundary conditions 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 $H^\alpha$-regularity ($\alpha>0$) assumption for the true solution, but also an effective approximation of normal harmonic vector fields regardless the topology of the domain. Results of seven numerical experiments are presented to demonstrate the performance of the PDWG algorithm, including one example on the computation of discrete normal harmonic vector fields.
翻译:本文件通过使用称为原始-二元弱哥尔金(PDWG)的有限元素技术,为具有正常边界条件的分曲线系统提供了一种数字方法。 div-curl系统PDWG的有限元素方案有两个突出特点,即它不仅为在低Häääalpha$-常规($alpha$0$)假设下用于真实解决方案的div-curl系统提供了准确和可靠的数字解决方案,而且为普通口腔矢量字段提供了有效的近似,而不管域的地形如何。还介绍了七个数字实验的结果,以证明PDWG算法的性能,包括一个计算离散正常向量字段的实例。