Adaptive discontinuous Galerkin approximation of optimal control problems governed by transient convection-diffusion equations
The authors study a posteriori error estimates of a control-constrained optimal control problem governed by a time-dependent convection-diffusion equation. The authors apply the symmetric interior penalty Galerkin method for the diffusion and the upwind discretization for the convection in order to discretize the optimization problem in space. The semi-smooth Newton method and the Moreau-Yosida regularization method are introduced to solve the optimality system. Some residual-based error estimators are also proposed for both approaches. Numerical examples are given to demonstrate the performance of the proposed error estimators.
scientific article; zbMATH DE number 7012416
scientific article