An HDG Method for Distributed Control of Convection Diffusion PDEs

Abstract

We propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a distributed optimal control problem governed by an elliptic convection diffusion PDE. We derive optimal a priori error estimates for the state, adjoint state, their fluxes, and the optimal control. We present 2D and 3D numerical experiments to illustrate our theoretical results.

arXiv admin note: substantial text overlap with arXiv:1712.10106, arXiv:1712.01403, arXiv:1712.02931

References in corpus (2)

• Error estimates for Dirichlet control problems in polygonal domains
• A Superconvergent Hybridizable Discontinuous Galerkin Method for Dirichlet Boundary Control of Elliptic PDEs

Cited by in corpus (8)

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• A Class of Embedded DG Methods for Dirichlet Boundary Control of Convection Diffusion PDEs
• Low Regularity Primal-Dual Weak Galerkin Finite Element Methods for Convection-Diffusion Equations
• Superconvergent HDG methods for Maxwell's equations via the $M$-decomposition
• On the superconvergence of a hydridizable discontinuous Galerkin method for the Cahn-Hilliard equation
• Optimal Control of Convection-Cooling and Numerical Implementation
• A hybridizable discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations
• Residual-type a posteriori error analysis of HDG methods for Neumann boundary control problems