求解带有奇异函数泊松问题的虚拟元方法

Virtual Element Method for Solving Poisson Problems with Singular Functions

摘要: 本文运用虚拟元方法求解带有奇异函数的泊松问题。首先给出了在多边形域上的二维泊松问题，构造非协调扩展虚拟元空间，对如何处理在多边形域的拐角处出现的奇异点进行讨论，给出自由度的计算方法，引入投影算子，得到相应的虚拟元离散格式，而后对虚拟元离散形式进行误差分析，最后在多边形网格上对带角奇点的L型域问题进行数值计算，结果证实了理论分析的正确性。

Abstract: In this paper, the virtual element method is used to solve the Poisson problem with singular func-tions. Firstly, the two-dimensional Poisson problem on the polygon domain is given, the noncon-forming extended the virtual element space is constructed , how to deal with the singularity at the corner of the polygon domain is discussed, the calculation method of the degree of freedom is given, and the projection operator is introduced to obtain the corresponding virtual element discrete format, and then the error analysis of the virtual element discrete form is carried out, and finally the numerical calculation of the type domain problem with angular singularity on the polygon mesh is carried out, and the results confirm the correctness of the theoretical analysis.