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Approximation of solution branchesfor semilinear bifurcation problems

Published online by Cambridge University Press:  15 August 2002

Laurence Cherfils
Laurence Cherfils*
Affiliation:
Laboratoire LMC-IMAG, B.P. 53, 38041 Grenoble Cedex 9, France. Present address: Laboratoire LMCA, Université de La Rochelle, avenue Marillac, 17042 La Rochelle Cedex 1, France.
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Abstract

This note deals with the approximation, by a P 1 finite element method with numerical integration,of solution curves of a semilinear problem. Because of both mixed boundary conditions and geometrical properties of the domain, some of the solutions do not belong to H 2. So, classical results for convergence lead to poor estimates. We show how to improve such estimates with the use of weighted Sobolev spaces together with a mesh“a priori adapted” to the singularity. For the H 1 or L 2-norms,we achieve optimal results.

Keywords

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 1 , January 1999 , pp. 191 - 207
Copyright
© EDP Sciences, SMAI, 1999

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