Convergence rate analysis of Galerkin approximation of inverse potential problem

Abstract In this work we analyze the inverse problem of recovering a space-dependent potential coefficient in an elliptic / parabolic from distributed observation. We establish novel (weighted) conditional stability estimates under very mild conditions on data. Then provide error analysis standard reconstruction scheme based output least-squares formulation with Tikhonov regularization (by H 1 -seminorm penalty), which is then discretized by Galerkin finite element method continuous piecewise linear elements space (and also backward Euler time for problems). present detailed discrete scheme, and convergence rates weighted L 2 ( Ω stretchy="false">) approximations respect to exact potential. The bounds explicitly depend noise level, parameter discretization parameter(s). Under suitable conditions, derive interior L 2 norms. employs sharp priori nonstandard test functions. Several numerical experiments are given complement theoretical analysis.