This work is devoted to the development of an efficient and robust technique for accurate capturing of the electric field in multi-material problems. The formulation is based on the finite element method enriched by the introduction of hat-type shape function within the elements crossed by the material interface. The peculiar feature of the proposed method consists in the direct employment of the hat-function that requires solely one additional degree of freedom per cut element for capturing the discontinuity in the electric potential gradient and, thus, the electric field. This additional degree of freedom is subsequently statically condensed element-wise prior to the assembly of the global discrete system. As a consequence, the graph of the system matrix remains the same as that of the standard finite element method. In order to guarantee the robust performance of the proposed method for a wide range of electrical material property ratios, it also accounts for the possible discontinuities among the neighboring cut elements that arise due to employing additional degrees of freedom fully local to the element. The method is tested using several examples solved on structured and unstructured grids. The proposed approach constitutes a basis for enriched FEM applicable to a wide range of electromagnetic problems.
Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization
The Center for Subsurface Modeling, The Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校计算工程与科学研究所地下建模中心）
An accurate finite element method for elliptic interface problems
University of Graz, Institute for Mathematics（格拉茨大学数学研究所）；Laboratoire de Mathématiques, Université Blaise Pascal (Clermont-Ferrand) and CNRS (UMR 6620)（布莱兹·帕斯卡大学（克莱蒙费朗）数学实验室及法国国家科学研究中心）
