A discontinuous Galerkin method for optimal control problems governed by a system of convection-diffusion PDEs with nonlinear reaction terms

Space-Time Discontinuous Galerkin Methods for Optimal Control Problems Governed by Time Dependent Diffusion-Convection-Reaction Equations

In this paper, space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convectionreaction equation without control constraints is studied. Time discretization is performed by discontinuous Galerkin method with piecewise constant and linear polynomials, while symmetric interior penalty Galerkin with upwinding is used for spa...

The Discontinuous Galerkin FEM for Convection-Diffusion Equations

Abstract. This paper is concerned with the analysis of the discontinuous Galerkin finite element method applied to nonstationary convection-diffusion problems with nonlinear convection and nonlinear diffusion. We generalize results from [2], where linear diffusion is assumed. Optimal error estimates are obtained for the L(H) norm and interelement jump terms, however due to the nonlinearity of t...

Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations

We study a posteriori error estimates for the numerical approximations of state constrained optimal control problems governed by convection diffusion equations, regularized by Moreau-Yosida and Lavrentiev-based techniques. The upwind Symmetric Interior Penalty Galerkin (SIPG) method is used as a discontinuous Galerkin (DG) discretization method. We derive different residual-based error indicato...

Adaptive Discontinuous Galerkin Approximation of Optimal Control Problems Governed by Transient Convection-Diffusion Equations

In this paper, we investigate an a posteriori error estimate of a control constrained optimal control problem governed by a time-dependent convection diffusion equation. Control constraints are handled by using the primal-dual active set algorithm as a semi-smooth Newton method or by adding a Moreau-Yosida-type penalty function to the cost functional. An adaptive mesh refinement indicated by a ...

Nečas Center for Mathematical Modeling Optimal L∞(L2)-error estimates for the DG method applied to nonlinear convection–diffusion problems with nonlinear diffusion