Optimal control under reduced regularity

Authors:
Thomas Apel;Gunter Winkler
Affiliations:
Universität der Bundeswehr München, Fak. für Mathematik und Bauinformatik, 85579 Neubiberg, Germany;Universität der Bundeswehr München, Fak. für Mathematik und Bauinformatik, 85579 Neubiberg, Germany
Venue:
Applied Numerical Mathematics
Year:
2009

Citing 8
Cited 2

Mesh refinement and windowing near edges for some elliptic problem

SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems
Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem

Computational Optimization and Applications
Superconvergence Properties of Optimal Control Problems

SIAM Journal on Control and Optimization
A variational discretization concept in control constrained optimization: the linear-quadratic case

Computational Optimization and Applications
Error Estimates for the Numerical Approximation of Boundary Semilinear Elliptic Control Problems

Computational Optimization and Applications
$L^\infty$-Estimates for Approximated Optimal Control Problems

SIAM Journal on Control and Optimization
Optimal Control of the Stokes Equations: A Priori Error Analysis for Finite Element Discretization with Postprocessing

SIAM Journal on Numerical Analysis

Optimal control of the Stokes equations: conforming and non-conforming finite element methods under reduced regularity

Computational Optimization and Applications
Finite element error estimates for Neumann boundary control problems on graded meshes

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper deals with a linear quadratic optimal control problem with elliptic PDE constraints in three-dimensional domains with singularities. It is proved that the optimal control can be calculated by the finite element method at a rate of O(h^2) provided that the mesh is sufficiently graded. The approximation of this control is computed from a piecewise constant approximation followed by a postprocessing step. Although the results are similar to the two-dimensional case, the proofs changed significantly.