Error estimates for Dirichlet control problems in polygonal domains

Abstract

The paper deals with finite element approximations of elliptic Dirichlet boundary control problems posed on two-dimensional polygonal domains. Error estimates are derived for the approximation of the control and the state variables. Special features of unconstrained and control constrained problems as well as general quasi-uniform meshes and superconvergence meshes are carefully elaborated. Compared to existing results, the convergence rates for the control variable are not only improved but also fully explain the observed orders of convergence in the literature. Moreover, for the first time, results in non-convex domains are provided.

Cited by in corpus (5)

• An HDG Method for Distributed Control of Convection Diffusion PDEs
• A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity
• Optimization Methods for Dirichlet Control Problems
• 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