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

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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 L 2-error estimates are of order o(h), which is optimal according with the \(C^{0,1}(\overline{\Omega})\) -regularity of the optimal control.

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Authors and Affiliations

  1. Dpto. de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, 39005, Santander, Spain

    Eduardo Casas

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  1. Eduardo Casas
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Correspondence to Eduardo Casas.

Additional information

Communicated by Jesus Carnicer and Juan Manuel Peña (Guest Editors)

This paper is dedicated to Mariano Gasca on the occasion of his 60th birthday

Mathematics subject classifications (2000)

65N30, 65N15, 49M05, 49M25.

This research was partially supported by Ministerio de Ciencia y Tecnología (Spain).

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Casas, E. Using piecewise linear functions in the numerical approximation of semilinear elliptic control problems. Adv Comput Math 26, 137–153 (2007). https://doi.org/10.1007/s10444-004-4142-0

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  • DOI: https://doi.org/10.1007/s10444-004-4142-0

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