4 research outputs found
A One Dimensional Elliptic Distributed Optimal Control Problem with Pointwise Derivative Constraints
We consider a one dimensional elliptic distributed optimal control problem
with pointwise constraints on the derivative of the state. By exploiting the
variational inequality satisfied by the derivative of the optimal state, we
obtain higher regularity for the optimal state under appropriate assumptions on
the data. We also solve the optimal control problem as a fourth order
variational inequality by a finite element method, and present the error
analysis together with numerical results
Finite Element Methods for Elliptic Distributed Optimal Control Problems with Pointwise State Constraints
Finite element methods for a model elliptic distributed optimal control
problem with pointwise state constraints are considered from the perspective of
fourth order boundary value problems
Finite Element Methods for One Dimensional Elliptic Distributed Optimal Control Problems with Pointwise Constraints on the Derivative of the State
We investigate finite element methods for one dimensional elliptic
distributed optimal control problems with pointwise constraints on the
derivative of the state formulated as fourth order variational inequalities for
the state variable. For the problem with Dirichlet boundary conditions, we use
an existing regularity result for the optimal state to
derive convergence for the approximation of the
optimal state in the norm. For the problem with mixed Dirichlet and
Neumann boundary conditions, we show that the optimal state belongs to
under appropriate assumptions on the data and obtain convergence for the
approximation of the optimal state in the norm
P 1 finite element methods for an elliptic optimal control problem with pointwise state constraints
We present theoretical and numerical results for two P finite element methods for an elliptic distributed optimal control problem on general polygonal/polyhedral domains with pointwise state constraints.