<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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 <italic>L∞</italic> norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.</p></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.

Topological Derivatives for Semilinear Elliptic Equations

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, France

Institute of Mechanical Engineering Problems, V.O., Bolshoi pr., 61, 199178, St. Petersburg, Russia

International Journal of Applied Mathematics and Computer Science

{"article-title":"Topological Derivatives for Semilinear Elliptic Equations"}

The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element...

Topological Derivatives for Semilinear Elliptic Equations

Published Online: Jul 08, 2009

Page range: 191 - 205

DOI: https://doi.org/10.2478/v10006-009-0016-4

Keywords
shape optimization, topological derivative, levelset method, variational inequality, asymptotic analysis

This content is open access.

Topological Derivatives for Semilinear Elliptic Equations

Published Online: Jul 08, 2009

Page range: 191 - 205

DOI: https://doi.org/10.2478/v10006-009-0016-4

Keywordsshape optimization, topological derivative, levelset method, variational inequality, asymptotic analysis

This content is open access.

Keywords
shape optimization, topological derivative, levelset method, variational inequality, asymptotic analysis