Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Finite-Dimensional Approximation of a Class of Constrained Nonlinear Optimal Control Problems
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Primal-Dual Strategy for Constrained Optimal Control Problems
SIAM Journal on Control and Optimization
A Posteriori Error Estimates for Convex Boundary Control Problems
SIAM Journal on Numerical Analysis
A Posteriori Error Estimates for Control Problems Governed by Stokes Equations
SIAM Journal on Numerical Analysis
A variational discretization concept in control constrained optimization: the linear-quadratic case
Computational Optimization and Applications
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Approximation of Boundary Control Problems on Curved Domains
SIAM Journal on Control and Optimization
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In this paper we study the finite element approximation of Dirichlet boundary control problems governed by elliptic PDEs. Based on a mixed variational scheme, we establish a mixed finite element approximation to the underlying optimal control problem. We consider the optimal control problems posed on both polygonal and general smooth domains, and we derive a priori error estimates for optimal control, state, and adjoint state. The optimal and quasi-optimal error estimates are obtained for problems on polygonal and smooth domains, respectively. Numerical experiments are provided to confirm our theoretical results.