Title

Finite element methods for one dimensional elliptic distributed optimal control problems with pointwise constraints on the derivative of the state

Document Type

Article

Publication Date

1-1-2020

Abstract

We investigate C 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 H52-ϵ regularity result for the optimal state to derive O(h12-ϵ) convergence for the approximation of the optimal state in the H norm. For the problem with mixed Dirichlet and Neumann boundary conditions, we show that the optimal state belongs to H under appropriate assumptions on the data and obtain O(h) convergence for the approximation of the optimal state in the H norm. 1 2 3 2

Publication Source (Journal or Book title)

Optimization and Engineering

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