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Enrichment of the nonconforming virtual element method with singular functions
Computer Methods in Applied Mechanics and Engineering ( IF 7.2 ) Pub Date : 2021-07-17 , DOI: 10.1016/j.cma.2021.114024
E. Artioli 1 , L. Mascotto 2
Affiliation  

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 that drastically trims the ill-conditioning of the final system.



中文翻译:

用奇异函数丰富非一致虚元方法

我们基于富含特殊奇异函数的近似空间构建了一种非一致性虚拟元方法 (ncVEM) 。这种丰富的 ncVEM 是为近似椭圆问题的解决方案量身定制的,椭圆问题由于域的几何形状而具有奇点与传统的扩展伽辽金方法不同,基于奇异函数的局部空间的丰富,没有使用统一的划分。相反,该方法的设计取决于非一致性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交化程序,它极大地减少了最终系统的病态。

更新日期:2021-07-18
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