Advances in Computational Mathematics

, Volume 26, Issue 1, pp 137–153

Using piecewise linear functions in the numerical approximation of semilinear elliptic control problems

Authors

    • Dpto. de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de TelecomunicaciónUniversidad de Cantabria
Article

DOI: 10.1007/s10444-004-4142-0

Cite this article as:
Casas, E. Adv Comput Math (2007) 26: 137. doi:10.1007/s10444-004-4142-0

Abstract

We study the numerical approximation of distributed optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. Piecewise linear finite elements are used to approximate the control as well as the state. We prove that the L2-error estimates are of order o(h), which is optimal according with the \(C^{0,1}(\overline{\Omega})\) -regularity of the optimal control.

Keywords

optimal controlsemilinear elliptic equationsnumerical approximationerror estimates

Copyright information

© Springer 2006