Immersed Virtual Element Methods for Elliptic Interface Problems in Two Dimensions
Immersed Virtual Element Methods for Elliptic Interface Problems in Two Dimensions
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DOI：
10.1007/s10915-022-01949-x
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发表时间：
2021-08
影响因子：
2.5
通讯作者：
Shuhao Cao;Long Chen;Ruchi Guo;F. Lin
中科院分区：
文献类型：
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作者：
Shuhao Cao;Long Chen;Ruchi Guo;F. Lin
结合贴体网格法和非贴体网格法的优点，提出了一种求解一类界面问题的浸入式虚拟单元法。首先生成背景贴体网格。在这些界面元素上，虚拟元素空间被构造为局部界面问题的解空间，并且可以为这些包含不连续系数的新空间建立精确序列。界面问题的间断系数被重塑为Hodge星形算子，这是将浸没虚函数投影到经典浸没有限元(IFE)函数以计算数值解的关键。建立了关于界面位置的稳健的先验收敛分析。该方法能够处理更复杂的界面单元配置，并且比传统的罚函数型IFE方法在求解Maxwell方程的界面问题时具有更好的性能。它还联系了各种方法之间的联系，如贴身法、IFE法、虚拟单元法等。
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 are the key to project immersed virtual functions to classic immersed finite element (IFE) functions for computing numerical solutions. An a priori convergence analysis is established robust with respect to the interface location. 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-interface problem arising from Maxwell equations. It also brings a connection between various methods such as body-fitted methods, IFE methods, virtual element methods, etc.