椭圆型方程系数反演问题的条件稳定性及离散正则化解的误差估计  

Conditional Stability of Coefficient Inversion for Elliptic Equation and Error Estimation for Discrete Regularization Solutions

作　　者：王兵贤 徐梅[1] 张玲萍[1] WANG Bing-xian;XU Mei;ZHANG Ling-ping(School of Mathematics and Statistics,Huaiyin Normal University,Huai'an Jiangsu 223300,China)

机构地区：[1]淮阴师范学院数学与统计学院,江苏淮安223300

出　　处：《淮阴师范学院学报（自然科学版）》2024年第3期195-198,共4页Journal of Huaiyin Teachers College(Natural Science Edition)

基　　金：国家自然科学基金项目(11501236);江苏省高校自然科学面上项目(18kJD110002);淮阴师范学院博士启动基金项目(31WBX00)。

摘　　要：椭圆型方程反问题是数学物理反问题领域的一个重要部分,基于整个区域的测量值,提出椭圆型方程模型中描述介质性质的系数反演问题,利用椭圆型方程弱解性质和Sobolev嵌入定理,得到反问题的条件稳定性估计.进一步利用Galerkin有限元离散优化问题,得到优化问题解的误差分析结果.The inverse problem of elliptic equations is an important part of the field of inverse problems for mathematical physics equations.Based on the measured values of the entire region,a coefficient inversion problem describing the properties of the medium in the elliptic equation model is proposed.By using the weak solution property of the elliptic equation and the sobolev embedding theorem,the conditional stability estimate of the inverse problem is obtained.Furthermore,the regularized output least-squares formulation is formulated for the elliptic inverse problem.And the continuous formulation is discretized by the Galerkin FEM with continuous piecewise linear elements,and the error analysis is provided.

关 键 词：椭圆型方程 系数 反演 条件稳定性 误差分析 

分 类 号：O175.2[理学—数学]