Error Estimates for the Numerical Approximation of Dirichlet Boundary Control for Semilinear Elliptic Equations

Authors:
Eduardo Casas;Jean-Pierre Raymond
Affiliations:
-;-
Venue:
SIAM Journal on Control and Optimization
Year:
2006

Citing 0
Cited 9

POD a-posteriori error estimates for linear-quadratic optimal control problems

Computational Optimization and Applications
Approximation of Boundary Control Problems on Curved Domains

SIAM Journal on Control and Optimization
A Priori Error Analysis for Linear Quadratic Elliptic Neumann Boundary Control Problems with Control and State Constraints

SIAM Journal on Control and Optimization
Mixed Finite Element Method for Dirichlet Boundary Control Problem Governed by Elliptic PDEs

SIAM Journal on Control and Optimization
A Paradox in the Approximation of Dirichlet Control Problems in Curved Domains.

SIAM Journal on Control and Optimization
On finite element error estimates for optimal control problems with elliptic PDEs

LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Boundary concentrated finite elements for optimal boundary control problems of elliptic PDEs

Computational Optimization and Applications
Second Order Analysis for Optimal Control Problems: Improving Results Expected From Abstract Theory

SIAM Journal on Optimization
A general theorem on error estimates with application to a quasilinear elliptic optimal control problem

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The control is the trace of the state on the boundary of the domain, which is assumed to be a convex, polygonal, open set in ${\mathbb R}^2$. Piecewise linear finite elements are used to approximate the control as well as the state. We prove that the error estimates are of order $O(h^{1 - 1/p})$ for some $p 2$, which is consistent with the $W^{1 - 1/p,p}(\Gamma)$-regularity of the optimal control.