Adaptive Finite Element Approximation for a Class of Parameter Estimation Problems (Journal of Computational Mathematics, 2019)
In this paper, we study adaptive finite element discretisation schemes for a class of parameter estimation problem. We propose to use adaptive multi-meshes in developing efficient algorithms for the estimation problem. We derive equivalent a posteriori error estimators for both the state and the control approximation, which particularly suit an adaptive multi-mesh finite element scheme. The error estimators are then implemented and tested with promising numerical results.
Keywords: Parameter estimation; Finite element approximation; Adaptive finite element methods; A posteriori error estimate.