scholarly journals Finite element error estimates on the boundary with application to optimal control

2014 ◽  
Vol 84 (291) ◽  
pp. 33-70 ◽  
Author(s):  
Thomas Apel ◽  
Johannes Pfefferer ◽  
Arnd Rösch
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Element Error

scholarly journals Finite element error estimates for one-dimensional elliptic optimal control by BV-functions

2019 ◽  
Vol 0 (0) ◽  
pp. 0-0 ◽  
Author(s):  
Dominik Hafemeyer ◽  
◽  
Florian Mannel ◽  
Ira Neitzel ◽  
Boris Vexler ◽  
...  
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
One Dimensional ◽  
Bv Functions ◽  
Elliptic Optimal Control ◽  
Element Error

scholarly journals New regularity results and finite element error estimates for a class of parabolic optimal control problems with pointwise state constraints

2020 ◽  
Author(s):  
Constantin Christof ◽  
Boris Vexler
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
State Constraints ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
First Order ◽  
Regularity Results ◽  
Parabolic Optimal Control ◽  
Element Error

We study first-order necessary optimality conditions and finite element error estimates for a class of distributed parabolic optimal control problems with pointwise state constraints. It is demonstrated that, if the bound in the state constraint and the differential operator in the governing PDE fulfill a certain compatibility assumption, then locally optimal controls satisfy a stationarity system that allows to significantly improve known regularity results for adjoint states and Lagrange multipliers in the parabolic setting. In contrast to classical approaches to first-order necessary optimality conditions for state-constrained problems, the main arguments of our analysis require neither a Slater point, nor uniform control constraints, nor differentiability of the objective function, nor a restriction of the spatial dimension. As an application of the established improved regularity properties, we derive new finite element error estimates for the dG(0)-cG(1)-discretization of a purely state-constrained linear-quadratic optimal control problem governed by the heat equation. The paper concludes with numerical experiments that confirm our theoretical findings.

Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations

2016 ◽  
Vol 8 (6) ◽  
pp. 1050-1071 ◽  
Author(s):  
Tianliang Hou ◽  
Li Li
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Elliptic Equations ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
Control Variable ◽  
The State ◽  
Control Problems ◽  
General Elliptic

AbstractIn this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive L2 and H–1-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.

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