Title: Adaptive Mixed Finite Element Methods for Distributed Optimal Control Problems
Venue: PSB 1207
Date and time: 8th August, 4 pm
Abstract: The talk will mainly focus on quasi-optimality of an adaptive conforming finite element method for the distributed optimal control problem governed by the mixed equation. The conforming lowest order Raviart-Thomas space and the space of piecewise constant functions are used to discretise the flux and displacement variables respectively in both state and adjoint equations. The control variable is discretized by incorporating a variational discretisation approach. The error equivalence results in suitable norms have been presented at both continuous and discrete levels, which helps us to prove the efficiency and reliability of the estimator. The optimal convergence rates are established based on an axiomatic framework which includes stability, reduction, discrete reliability, and quasi orthogonality of the proposed error estimator. Finally the numerical experiments confirm the theoretical findings.