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

2025/06/14 by Satyajith Bommana Boyana, Thomas Lewis, Boyana, Satyajith Bommana +5 · 1 citation
Computer Science · Engineering · Mathematics · #65K15 #65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2506.12330

openalex publication_date 2025/06/14 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

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 L² norm of the control variable. Numerical experiments are provided to demonstrate the robustness and effectiveness of the developed scheme.

Citations

• Multigrid preconditioning for discontinuous Galerkin discretizations of an elliptic optimal control problem with a convection-dominated state equation
• Convergence analysis of novel discontinuous Galerkin methods for a convection dominated problem
• Robust Multigrid Methods for Discontinuous Galerkin Discretizations of an Elliptic Optimal Control Problem
• A Frame Work for the Error Analysis of Discontinuous Finite Element Methods for Elliptic Optimal Control Problems and Applications to C⁰ IP methods
• Discontinuous Galerkin finite element differential calculus and applications to numerical solutions of linear and nonlinear partial differential equations
• The Finite Element Method for Elliptic Problems
• Nonlinear total variation based noise removal algorithms

Cited by

• Convergence analysis of a balancing domain decomposition method for an elliptic optimal control problem with HDG discretizations

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