Numerische Mathematik

, Volume 132, Issue 4, pp 691–720 | Cite as

Error estimates for optimal control problems of a class of quasilinear equations arising in variable viscosity fluid flow

  • Juan Carlos De Los ReyesEmail author
  • Vili Dhamo


We consider optimal control problems of quasilinear elliptic equations with gradient coefficients arising in variable viscosity fluid flow. The state equation is monotone and the controls are of distributed type. We prove that the control-to-state operator is twice Fréchet differentiable for this class of equations. A finite element approximation is studied and an estimate of optimal order h is obtained for the control. The result makes use of the distributed structure of the controls, together with a regularity estimate for elliptic equations with Hölder coefficients and a second order sufficient optimality condition. The paper ends with a numerical experiment, where the approximation order is computationally tested.

Mathematics Subject Classification

65N30 49K20 35J62 76A05 



We would like to thank Christian Meyer (TU Dortmund) for pointing out the extra regularity result by Konrad Gröger [23]. We are also grateful to the anonymous referees for the careful reading of the manuscript and their valuable suggestions which lead to an improved version of the paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Research Center on Mathematical Modelling (MODEMAT)Escuela Politécnica Nacional de QuitoQuitoEcuador
  2. 2.BerlinGermany

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