A Posteriori Error Estimation Based on Primal-Dual Formulations

Recently, based on the Prage-Synge identity, a posteriori error estimator for finite element

approximations to the diffusion equation has been developed with the reliability constant to be one.

In this talk, I will talk about its generalization: error estimation based on the gap between

approximations of primal and dual problems and the localization of these estimators.

Generalization of the idea to the a posteriori error estimation of the reduced basis method will also be discussed.