A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity

Abstract

In the first part of this work, we analyzed a Dirichlet boundary control problem for an elliptic convection diffusion PDE and proposed a new hybridizable discontinuous Galerkin (HDG) method to approximate the solution. For the case of a 2D polygonal domain, we also proved an optimal superlinear convergence rate for the control under certain assumptions on the domain and on the target state. In this work, we revisit the convergence analysis without these assumptions; in this case, the solution can have low regularity and we use a different analysis approach. We again prove an optimal convergence rate for the control, and present numerical results to illustrate the convergence theory.

References in corpus (1)

• Error estimates for Dirichlet control problems in polygonal domains

Cited by in corpus (7)

• An HDG Method for Dirichlet Boundary Control of Convection Dominated Diffusion PDE
• Analysis of a hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system
• 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
• Optimal Control of Convection-Cooling and Numerical Implementation
• On the superconvergence of a hydridizable discontinuous Galerkin method for the Cahn-Hilliard equation