scholarly journals Adaptive finite element methods for an optimal control problem involving Dirac measures

2017 ◽  
Vol 137 (1) ◽  
pp. 159-197 ◽  
Author(s):  
Alejandro Allendes ◽  
Enrique Otárola ◽  
Richard Rankin ◽  
Abner J. Salgado
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Finite Element Methods ◽  
Adaptive Finite Element ◽  
Adaptive Finite Element Methods ◽  
Dirac Measures

scholarly journals Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Zuliang Lu
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
A Posteriori Error Estimates ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Adaptive Finite Element ◽  
Element Discretization ◽  
Semilinear Parabolic

The aim of this work is to study the semidiscrete finite element discretization for a class of semilinear parabolic integrodifferential optimal control problems. We derive a posteriori error estimates inL2(J;L2(Ω))-norm andL2(J;H1(Ω))-norm for both the control and coupled state approximations. Such estimates can be used to construct reliable adaptive finite element approximation for semilinear parabolic integrodifferential optimal control problem. Furthermore, we introduce an adaptive algorithm to guide the mesh refinement. Finally, a numerical example is given to demonstrate the theoretical results.

scholarly journals P 1 finite element methods for an elliptic optimal control problem with pointwise state constraints

2018 ◽  
Vol 40 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Susanne C Brenner ◽  
Li-yeng Sung ◽  
Joscha Gedicke
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Finite Element Methods ◽  
State Constraints ◽  
Distributed Optimal Control ◽  
Pointwise State Constraints ◽  
Elliptic Optimal Control Problem ◽  
Elliptic Optimal Control

Abstract We present theoretical and numerical results for two $P_1$ finite element methods for an elliptic distributed optimal control problem on general polygonal/polyhedral domains with pointwise state constraints.

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