Convergence Analysis of a Dual-Wind Discontinuous Galerkin Method for an Elliptic Optimal Control Problem with Control Constraints

TL;DR

This paper presents a convergence analysis of a symmetric dual-wind discontinuous Galerkin method applied to elliptic optimal control problems with control constraints, providing error estimates and numerical validation.

Contribution

The paper introduces a novel symmetric DWDG method for elliptic control problems and derives rigorous error estimates for the state, adjoint state, and control variables.

Findings

Error estimates in energy and $L^2$ norms for state, adjoint, and control

Numerical experiments confirm robustness and effectiveness

Method effectively handles control constraints in elliptic PDEs

Abstract

This paper investigates a symmetric dual-wind discontinuous Galerkin (DWDG) method for solving an elliptic optimal control problem with control constraints. The governing constraint is an elliptic partial differential equation (PDE), which is discretized using the symmetric DWDG approach. We derive error estimates in the energy norm for both the state and the adjoint state, as well as in the $L^2$ norm of the control variable. Numerical experiments are provided to demonstrate the robustness and effectiveness of the developed scheme.