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The focus of this paper is on the concurrent reconstruction of both thediffusion and potential coefficients present in an elliptic/parabolic equation,utilizing two internal measurements of the solutions. A decoupled algorithm isconstructed to sequentially recover these two parameters. In the first step, weimplement a straightforward reformulation that results in a standard problem ofidentifying the diffusion coefficient. This coefficient is then numericallyrecovered, with no requirement for knowledge of the potential, by utilizing anoutput least-square method coupled with finite element discretization. In thesecond step, the previously recovered diffusion coefficient is employed toreconstruct the potential coefficient, applying a method similar to the firststep. Our approach is stimulated by a constructive conditional stability, andwe provide rigorous a priori error estimates in $L^2(\Omega)$ for the recovereddiffusion and potential coefficients. Our approach is stimulated by aconstructive conditional stability, and we provide rigorous a priori errorestimates in $L^2(\Omega)$ for the recovered diffusion and potentialcoefficients. To derive these estimates, we develop a weighted energy argumentand suitable positivity conditions. These estimates offer a beneficial guidefor choosing regularization parameters and discretization mesh sizes, inaccordance with the noise level. Some numerical experiments are presented todemonstrate the accuracy of the numerical scheme and support our theoreticalresults.

Numerical Reconstruction of Diffusion and Potential Coefficients from Two Observations: Decoupled Recovery and Error Estimates