论文标题
具有单数函数的不合格虚拟元素方法的丰富
Enrichment of the nonconforming virtual element method with singular functions
论文作者
论文摘要
我们基于具有特殊单数函数的近似空间构建一个不合格的虚拟元素方法（NCVEM）。该富集的NCVEM是针对椭圆形问题的溶液的近似而定制的，椭圆问题的溶液由于域的几何形状而具有奇异性。与传统的扩展Galerkin方法不同，基于具有单数功能的局部空间的丰富，不采用统一分区。相反，该方法的设计取决于不合格的虚拟元素空间的特殊结构。我们讨论了该方法的理论分析，并通过几个数值实验来支持它。我们还提出了一个正定化的过程，彻底修剪了最终系统的不良条件。
We construct a nonconforming virtual element method (ncVEM) based on approximation spaces that are enriched with special singular functions. This enriched ncVEM is tailored for the approximation of solutions to elliptic problems, which have singularities due to the geometry of the domain. Differently from the traditional extended Galerkin method approach, based on the enrichment of local spaces with singular functions, no partition of unity is employed. Rather, the design of the method hinges upon the special structure of the nonconforming virtual element spaces. We discuss the theoretical analysis of the method and support it with several numerical experiments. We also present an orthonormalization procedure drastically trimming the ill-conditioning of the final system.
