scholarly journals Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's

2009 ◽  
Vol 44 (1) ◽  
pp. 189-206 ◽  
Author(s):  
Konstantinos Chrysafinos
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Discontinuous Galerkin ◽  
Galerkin Approximations ◽  
Semilinear Parabolic

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 A Mixed Discontinuous Galerkin Approximation of Time Dependent Convection Diffusion Optimal Control Problem

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Qingjin Xu ◽  
Zhaojie Zhou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Discontinuous Galerkin ◽  
Mixed Finite Element ◽  
Galerkin Approximation ◽  
Control Variable ◽  
The State ◽  
Time Dependent ◽  
Convection Diffusion

In this paper, we investigate a mixed discontinuous Galerkin approximation of time dependent convection diffusion optimal control problem with control constraints based on the combination of a mixed finite element method for the elliptic part and a discontinuous Galerkin method for the hyperbolic part of the state equation. The control variable is approximated by variational discretization approach. A priori error estimates of the state, adjoint state, and control are derived for both semidiscrete scheme and fully discrete scheme. Numerical example is given to show the effectiveness of the numerical scheme.

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