The virtual element calculation for a class of two-dimensional elliptic interface problems

The elliptic interface problem is a classical model problem that frequently occurs in numerical simulations in fields such as mechanics, materials science, and biochemistry. This model problem is characterized by discontinuous coefficients and irregular interfaces. The use of the virtual element method to solve three-dimensional elliptic interface problems is more suitable for general polyhedral meshes compared to traditional finite element methods, allowing for greater freedom and diversity in mesh selection. Based on this characteristic, this paper presents the computational formula for solving a class of three-dimensional elliptic interface problems using the virtual element method and conducts numerical experiments using three different polyhedral meshes. The numerical results demonstrate that the virtual element method is effective for this problem.