Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem

Authors:
Nadir Arada;Eduardo Casas;Fredi Tröltzsch
Affiliations:
Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany;Departamento de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, 39005 Santander, Spain;Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany
Venue:
Computational Optimization and Applications
Year:
2002

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Abstract

We study the numerical approximation of distributed nonlinear optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. Our main result are error estimates for optimal controls in the maximum norm. Characterization results are stated for optimal and discretized optimal control. Moreover, the uniform convergence of discretized controls to optimal controls is proven under natural assumptions.