凹角区域外椭圆边值问题的局部人工边界条件  

Local Artificial Boundary Conditions for the Elliptic Boundary Value Problem in an Exterior Concave Region

作　　者：段良晓 刘保庆[1] DUAN Liangxiao;LIU Baoqing(School of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing Jiangsu 210000,China)

机构地区：[1]南京财经大学应用数学学院,江苏南京210023

出　　处：《淮阴师范学院学报（自然科学版）》2024年第4期297-303,307,共8页Journal of Huaiyin Teachers College(Natural Science Edition)

基　　金：国家自然科学基金青年基金项目(11401296)。

摘　　要：针对无界凹角区域上的调和方程,本文采用局部人工边界条件进行有限元法逼近.将无边界问题转化为更易处理的有边界问题,为解决复杂PDE问题提供了新的路径,减轻了无边界带来的计算负担,从而提升了数值求解的效率与精确度.同时给出了该方程自然边界元与有限元耦合的变分形式与数值方法以及近似解的误差估计.最后进行了数值实验,验证了该方法的有效性和可行性。This article employs local artificial boundary conditions for the approximation of the finite element method in solving the harmonic equation over an unbounded concave region.This approach transforms an unbounded problem into a more manageable bounded problem,paving a new avenue for tackling complex PDE issues.It not only alleviates the computational burden associated with boundarylessness but also enhances the efficiency and accuracy of numerical solutions.The paper further elucidates the variational formulation and numerical strategies for coupling natural boundary elements with finite elements for this equation,alongside an estimation of the approximation error.Numerical experiments are conducted to validate the efficacy and feasibility of the proposed method.

关 键 词：调和方程 局部人工边界条件 耦合法 

分 类 号：O241.82[理学—计算数学]