1,505 research outputs found
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
Discontinuous Galerkin Methods for an Elliptic Optimal Control Problem with a General State Equation and Pointwise State Constraints
We investigate discontinuous Galerkin methods for an elliptic optimal control
problem with a general state equation and pointwise state constraints on
general polygonal domains. We show that discontinuous Galerkin methods for
general second-order elliptic boundary value problems can be used to solve the
elliptic optimal control problems with pointwise state constraints. We
establish concrete error estimates and numerical experiments are shown to
support the theoretical results
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
Superconvergence for Neumann boundary control problems governed by semilinear elliptic equations
This paper is concerned with the discretization error analysis of semilinear
Neumann boundary control problems in polygonal domains with pointwise
inequality constraints on the control. The approximations of the control are
piecewise constant functions. The state and adjoint state are discretized by
piecewise linear finite elements. In a postprocessing step approximations of
locally optimal controls of the continuous optimal control problem are
constructed by the projection of the respective discrete adjoint state.
Although the quality of the approximations is in general affected by corner
singularities a convergence order of is proven for domains
with interior angles smaller than using quasi-uniform meshes. For
larger interior angles mesh grading techniques are used to get the same order
of convergence
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