SIAM Journal on Mathematical Analysis
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Primal-Dual Active Set Strategy for a General Class of Constrained Optimal Control Problems
SIAM Journal on Optimization
Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem
Computational Optimization and Applications
Superconvergence Properties of Optimal Control Problems
SIAM Journal on Control and Optimization
A variational discretization concept in control constrained optimization: the linear-quadratic case
Computational Optimization and Applications
Error Estimates for the Numerical Approximation of Boundary Semilinear Elliptic Control Problems
Computational Optimization and Applications
$L^\infty$-Estimates for Approximated Optimal Control Problems
SIAM Journal on Control and Optimization
SIAM Journal on Numerical Analysis
SIAM Journal on Control and Optimization
Optimal control under reduced regularity
Applied Numerical Mathematics
$L^\infty$-Error Estimates on Graded Meshes with Application to Optimal Control
SIAM Journal on Control and Optimization
Least-squares finite-element methods for optimization and control problems for the stokes equations
Computers & Mathematics with Applications
A Legendre-Galerkin Spectral Method for Optimal Control Problems Governed by Stokes Equations
SIAM Journal on Numerical Analysis
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This paper deals with a control-constrained linear-quadratic optimal control problem governed by the Stokes equations. It is concerned with situations where the gradient of the velocity field is not bounded. The control is discretized by piecewise constant functions. The state and the adjoint state are discretized by finite element schemes that are not necessarily conforming. The approximate control is constructed as projection of the discrete adjoint velocity in the set of admissible controls. It is proved that under certain assumptions on the discretization of state and adjoint state this approximation is of order 2 in L 2(驴). As first example a prismatic domain with a reentrant edge is considered where the impact of the edge singularity is counteracted by anisotropic mesh grading and where the state and the adjoint state are approximated in the lower order Crouzeix-Raviart finite element space. The second example concerns a nonconvex, plane domain, where the corner singularity is treated by isotropic mesh grading and state and adjoint state can be approximated by a couple of standard element pairs.