A posteriori error estimates for discontinuous Galerkin approximation of non-stationary convection-diffusion optimal control problems

Abstract

In this paper, we investigate a discontinuous Galerkin finite element approximation of non-stationary convection dominated diffusion optimal control problems with control constraints. The state variable is approximated by piecewise linear polynomial space and the control variable is discretized by variational discretization concept. Backward Euler method is used for time discretization. With the help of elliptic reconstruction technique residual type a posteriori error estimates are derived for state variable and adjoint state variable, which can be used to guide the mesh refinement in the adaptive algorithm. Numerical experiment is presented, which indicates the good behaviour of the a posteriori error estimators.

Keywords:

• non-stationary convection-diffusion equations
• optimal control problem
• discontinuousGalerkin method
• elliptic reconstruction
• a posteriori error estimate

2010 AMS Subject Classification:

• 65N30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China under Grants 11301311 and 11471196.