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Author: Meyer, Christian × Subject: finite elements ×

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    Finite element error analysis for state-constrained optimal control of the Stokes equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Reyes, Juan Carlos de los; Meyer, Christian; Vexler, Boris
    An optimal control problem for 2d and 3d Stokes equations is investigated with pointwise inequality constraints on the state and the control. The paper is concerened with the full discretization of the control problem allowing for different types of discretization of both the control and the state. For instance, piecewise linear and continuous approximations of the control are included in the present theory. Under certain assumptions on the $L^infty$-error of the finite element discretization of the state, error estimates for the control are derived which can be seen to be optimal since their order of convergence coincides with the one of the interpolation error. The assumptions of the $L^infty$-finite-element-error can be verified for different numerical settings. The theoretical results are confirmed by numerical examples.
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    A priori error analysis for state constrained boundary control problems : Part I: Control discretization
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Krumbiegel, Klaus; Meyer, Christian; Rösch, Arnd
    This is the first of two papers concerned with a state-constrained optimal control problems with boundary control, where the state constraints are only imposed in an interior subdomain. We apply the virtual control concept introduced in [20] to regularize the problem. The arising regularized optimal control problem is discretized by finite elements and linear and continuous ansatz functions for the boundary control. In the first part of the work, we investigate the errors induced by the regularization and the discretization of the boundary control. The second part deals with the error arising from discretization of the PDE. Since the state constraints only appear in an inner subdomain, the obtained order of convergence exceeds the known results in the field of a priori analysis for state-constrained problems