Advances in Computational Mathematics

, Volume 26, Issue 1, pp 137–153

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


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


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.


optimal controlsemilinear elliptic equationsnumerical approximationerror estimates

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© Springer 2006

Authors and Affiliations

  1. 1.Dpto. de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de TelecomunicaciónUniversidad de CantabriaSantanderSpain