一类三维椭圆界面问题的虚单元计算

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

椭圆界面问题是一种常出现在力学、材料科学、生物化学等领域的数值模拟中的经典模型问题。该模型问题具有间断系数和不规则界面两大特点。采用虚单元方法求解三维椭圆界面问题,与传统有限元法相比,该方法更适用于一般的多面体网格,这使得网格的选取变得自由与多样。基于这种特点,给出虚单元法求解一类三维椭圆界面问题的计算公式,并使用3种不同的多面体网格完成数值实验。数值结果表明,虚单元方法应用于该问题是有效的。

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.