Adaptive finite element approximation for a class of parameter estimation problems

In this paper, we investigate the finite element approximation of a class of parameter estimation problems which are the form of performance as the optimal control problems governed by bilinear parabolic equations. We propose to use adaptive multi-meshes in developing efficient algorithms for the estimation problems. We derive a posteriori error estimators for both the control and state approximations, which particularly suit an adaptive multi-meshes finite element scheme. The error estimators are then implemented and tested with promising numerical results.