Space-Time Discontinuous Galerkin Solution of Convection Dominated Optimal Control Problems

TL;DR

This paper develops a space-time discontinuous Galerkin finite element method for solving unsteady diffusion-convection-reaction optimal control problems with control constraints, demonstrating confirmed convergence rates through numerical results.

Contribution

It introduces a novel space-time discontinuous Galerkin approach for constrained optimal control problems governed by complex PDEs.

Findings

Confirmed convergence rates through numerical experiments

Effective handling of control constraints in complex PDEs

Demonstrated stability and accuracy of the method

Abstract

In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with 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 space discretization. The numerical results presented confirm the theoretically observed convergence rates.