The inverse problem of elliptic equations is an important part of the field of inverse prob-lems for mathematical physics equations.Based on the measured values of the entire region,a coeffi-cient inversion problem describing the properties of the medium in the elliptic equation model is pro-posed.By using the weak solution property of the elliptic equation and the sobolev embedding theo-rem,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 for-mulation is discretized by the Galerkin FEM with continuous piecewise linear elements,and the error analysis is provided.
维普
万方数据