Quasi-optimal adaptive mixed finite element methods for controlling natural norm errors

Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems

We will investigate the adaptive mixed finite element methods for parabolic optimal control problems. The state and the costate are approximated by the lowest-order Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise constant elements. We derive a posteriori error estimates of themixed finite element solutions for optimal control problems. Such a posteriori ...

Convergence and quasi-optimality of an adaptive finite element method for controlling L 2 errors

Convergence and quasi-optimality of an adaptive finite element method for controlling L2 errors ⋆ Alan Demlow1, Rob Stevenson2 1 Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, KY 40506–0027 ([email protected]) 2 Korteweg-de Vries (KdV) Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands (R.P.Stevenson@...

Adaptive Finite Element Methods for Optimal

Adaptive Finite Element Methods for Optimal Control

We develop a new approach towards error control and adaptivity for nite element discretizations in optimization problems governed by partial diierential equations. Using the Lagrangian formalism the goal is to compute stationary points of the rst-order necessary opti-mality conditions. The mesh adaptation is driven by residual-based a posteriori error estimates derived by duality arguments. Thi...

An optimal adaptive mixed finite element method

Various applications in fluid dynamics and computational continuum mechanics motivate the development of reliable and efficient adaptive algorithms for mixed finite element methods. In order to save degrees of freedom, not all but just a selection of finite element domains are refined. Hence the fundamental question of convergence as well as the question of optimality require new mathematical a...