Topological Derivatives for Semilinear Elliptic Equations

  • Authors:

  • Mohamed Iguernane;Serguei Nazarov;Jean-Rodolphe Roche;Jan Sokolowski;Katarzyna Szulc

  • Affiliations:

  • Laboratoire de Mathématiques, Institut Elie Cartan Université Henri Poincaré, UMR 7502 Nancy-Université-CNRS-INRIA Nancy 1, B.P. 239, 54506 Vandoeuvre lès Nancy Cedex, Fra ...;Institute of Mechanical Engineering Problems, V.O., Bolshoi pr., 61, 199178, St. Petersburg, Russia;Laboratoire de Mathématiques, Institut Elie Cartan Université Henri Poincaré, UMR 7502 Nancy-Université-CNRS-INRIA Nancy 1, B.P. 239, 54506 Vandoeuvre lès Nancy Cedex, Fra ...;Laboratoire de Mathématiques, Institut Elie Cartan Université Henri Poincaré, UMR 7502 Nancy-Université-CNRS-INRIA Nancy 1, B.P. 239, 54506 Vandoeuvre lès Nancy Cedex, Fra ...;Laboratoire de Mathématiques, Institut Elie Cartan Université Henri Poincaré, UMR 7502 Nancy-Université-CNRS-INRIA Nancy 1, B.P. 239, 54506 Vandoeuvre lès Nancy Cedex, Fra ...

  • Venue:
  • International Journal of Applied Mathematics and Computer Science
  • Year:
  • 2009

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Abstract

The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L∞ norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.