求解二维膜壳问题的虚拟元方法  

Virtual Element Method for Solving Two-Dimensional Membrane-Shell Problems

作　　者：马俊驰 刘洋[1] 索宇洋 MA Jun-chi;LIU Yang;SUO Yu-yang(School of Mathematics,Liaoning Normal University,Dalian 116029,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《数学的实践与认识》2024年第4期235-243,共9页Mathematics in Practice and Theory

基　　金：辽宁省教育厅基本科研项目(JYTMS20231045);国家自然科学基金青年项目(12001256)。

摘　　要：采用虚拟元方法求解二维膜壳问题.首先构造虚拟元空间,给出空间中函数自由度的计算方法.其次引入相应的投影算子,确定双线性形式的虚拟元离散格式,讨论解的存在唯一性.然后对离散形式进行误差估计.最后给出数值算例,给出不同网格剖分下的数值解,通过不同范数意义下的绝对误差,可以看出随着膜壳剖分的细化,误差逐渐变小,验证了理论分析的有效性.In this paper,the virtual element method is used to solve the two-dimensional membrane shell problem.Firstly,the virtual element space is constructed and the method to calculate the degree of freedom of the function in the space is given.Secondly,the corresponding projection operator is introduced to determine the bilinear virtual element discrete scheme,the existence and uniqueness of the solution are discussed.Then we estimate the error of the discrete scheme.Finally,a numerical example is given to obtain the numerical solution under different mesh sections.Through the absolute error under different norms,it can be seen that with the refinement of shell sections,the error gradually decrease,which verifies the validity of the theoretical analysis.

关 键 词：膜壳问题 虚拟元 投影算子 误差分析 

分 类 号：O241.82[理学—计算数学]