Space-Time Adaptive Wavelet Methods for Optimal Control Problems Constrained by Parabolic Evolution Equations

2011 ◽  
Vol 49 (3) ◽  
pp. 1150-1170 ◽  
Author(s):  
Max D. Gunzburger ◽  
Angela Kunoth
Keyword(s):  
Optimal Control ◽  
Evolution Equations ◽  
Optimal Control Problems ◽  
Space Time ◽  
Control Problems ◽  
Adaptive Wavelet ◽  
Parabolic Evolution Equations ◽  
Wavelet Methods

scholarly journals Commutative properties for conservative space-time DG discretizations of optimal control problems involving the viscous Burgers equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xenia Kerkhoff ◽  
Sandra May
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Burgers Equation ◽  
Adjoint Equation ◽  
State Equation ◽  
Space Time ◽  
The State ◽  
Control Problems ◽  
Viscous Term ◽  
Distributed Optimal Control Problems

<p style='text-indent:20px;'>We consider one-dimensional distributed optimal control problems with the state equation being given by the viscous Burgers equation. We discretize using a space-time discontinuous Galerkin approach. We use upwind flux in time and the symmetric interior penalty approach for discretizing the viscous term. Our focus is on the discretization of the convection terms. We aim for using conservative discretizations for the convection terms in both the state and the adjoint equation, while ensuring that the approaches of discretize-then-optimize and optimize-then-discretize commute. We show that this is possible if the arising source term in the adjoint equation is discretized properly, following the ideas of well-balanced discretizations for balance laws. We support our findings by numerical results.</p>

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