Abstract
We discuss error estimates for the numerical analysis of Neumann boundary control problems. We present some known results about piecewise constant approximations of the control and introduce some new results about continuous piecewise linear approximations. We obtain the rates of convergence in L 2(Γ). Error estimates in the uniform norm are also obtained. We also discuss the semidiscretization approach as well as the improvement of the error estimates by making an extra assumption over the set of points corresponding to the active control constraints.
Paper written with financial support of Ministerio de Ciencia y Tecnología (Spain).
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Casas, E., Mateos, M. (2006). Error Estimates for the Numerical Approximation of Boundary Semilinear Elliptic Control Problems. Continuous Piecewise Linear Approximations. In: Ceragioli, F., Dontchev, A., Furuta, H., Marti, K., Pandolfi, L. (eds) Systems, Control, Modeling and Optimization. CSMO 2005. IFIP International Federation for Information Processing, vol 202. Springer, Boston, MA . https://doi.org/10.1007/0-387-33882-9_9
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DOI: https://doi.org/10.1007/0-387-33882-9_9
Publisher Name: Springer, Boston, MA
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