Error Estimates for the Numerical Approximation of Boundary Semilinear Elliptic Control Problems

Authors:
Eduardo Casas;Mariano Mateos;Fredi Tröltzsch
Affiliations:
Departamento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, Santander, Spain 39071;Departamento de Matemáticas, E.P.S.I. de Gijón, Universidad de Oviedo, Campus de Viesques, Gijón, Spain 33203;Institut für Mathematik, Technische Universität Berlin, Berlin, Germany 10623
Venue:
Computational Optimization and Applications
Year:
2005

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Abstract

We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The analysis of the approximate control problems is carried out. The uniform convergence of discretized controls to optimal controls is proven under natural assumptions by taking piecewise constant controls. Finally, error estimates are established and some numerical experiments, which confirm the theoretical results, are performed.