This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated initially. On those interface elements, virtual element spaces are constructed as solution spaces to local interface problems, and exact sequences can be established for these new spaces involving discontinuous coefficients. The discontinuous coefficients of interface problems are recast as Hodge star operators that is the key to project immersed virtual functions to classic immersed finite element (IFE) functions for computing numerical solutions. The proposed method is capable of handling more complicated interface element configuration, and provides better performance than the conventional penalty-type IFE method for the H(curl)-interface problem. It also brings a connection between various methods such as body-fitted methods, IFE methods, and virtual element methods etc.
翻译:本文提供了解决一组界面问题的隐蔽虚拟元素方法, 它将机体适合的网格方法和不合适的网格方法的优势结合起来。 最初产生了一个背景体格网格。 在这些界面元素上, 虚拟元素空间被构建为解决本地界面问题的解决方案空间, 并为这些涉及不连续系数的新空间设定了精确的序列。 界面问题的不连续系数被重新定位为 Hodge 恒星操作员, 这是将嵌入的虚拟函数投射为典型的浸入的有限元素( IFE) 函数以计算数字解决方案的关键 。 拟议的方法能够处理更复杂的界面元素配置, 并且比 H( crurl) 界面问题的常规的IFE 处罚类型方法提供更好的性能。 它还将机体适应方法、 IFE 方法和虚拟元素方法等各种方法联系起来 。