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.
翻译:我们根据近似空间构建一种不兼容的虚拟元素方法(ncVEM),该方法以具有特殊单元功能的近似空间丰富。这种浓缩的ncVEM是专门为近似外省问题的解决方案而设计的,这些解决方案由于域的几何而具有独特性。不同于传统的扩大的Galerkin方法方法,该方法基于以独功能丰富地方空间,没有使用统一分割法。相反,该方法的设计取决于不兼容虚拟元素空间的特殊结构。我们讨论该方法的理论分析,并用若干数字实验来支持该方法。我们还提出一个异常化程序,对最终系统的错误调节进行急剧调整。