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