Roland Becker, Professor, University of Pau, France

Shipeng Mao, Professor

Adaptive finite element methods for parameter estimation

16:30-17:30 December 11(Monday), Tencent Meeting: 369-716-119

In this talk we consider parameter-dependent elliptic partial differential equations with a finite number of parameters. The unknown parameters are sought for by minimizing a least-squares involving data/measurements. The underlying PDE is discretized by a conforming finite element method on a sequence of adaptive meshes, which are constructed by means of an error estimator.

Here we propose an estimator for the error in parameter only. This in contrast to known estimators from the literature, which in addition control the energy-norm of the state and co-state. Our reason for doing so is that the last mentioned terms are generally of slower speed of convergence.

After some motivation, we first discuss goal-oriented error estimation, then consider the parameter estimation problem, and finally we will discuss some open problems.