Immersed Virtual Element Methods for Elliptic Interface Problems

Shuhao Cao, Long Chen, Ruchi Guo, and Frank Lin


arXiv   Bibtex coming soon


 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.