1,505 research outputs found

    Discontinuous Galerkin Methods for an Elliptic Optimal Control Problem with a General State Equation and Pointwise State Constraints

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    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

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    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 C1C^1 finite element method, and present the error analysis together with numerical results

    Superconvergence for Neumann boundary control problems governed by semilinear elliptic equations

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    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 h2lnh3/2h^2|\ln h|^{3/2} is proven for domains with interior angles smaller than 2π/32\pi/3 using quasi-uniform meshes. For larger interior angles mesh grading techniques are used to get the same order of convergence
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