Approximation of solution branches for semilinear bifurcation problems

Laurence Cherfils

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 33, Issue: 1, page 191-207
  • ISSN: 0764-583X

Abstract

top
This note deals with the approximation, by a P1 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 H2. 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 H1 or L2-norms, we achieve optimal results.

How to cite

top

Cherfils, Laurence. "Approximation of solution branches for semilinear bifurcation problems." ESAIM: Mathematical Modelling and Numerical Analysis 33.1 (2010): 191-207. <http://eudml.org/doc/197470>.

@article{Cherfils2010,
abstract = { This note deals with the approximation, by a P1 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 H2. 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 H1 or L2-norms, we achieve optimal results. },
author = {Cherfils, Laurence},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {semilinear problem; bifurcation; singularity; adaptive finite element method; numerical examples; error estimates},
language = {eng},
month = {3},
number = {1},
pages = {191-207},
publisher = {EDP Sciences},
title = {Approximation of solution branches for semilinear bifurcation problems},
url = {http://eudml.org/doc/197470},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Cherfils, Laurence
TI - Approximation of solution branches for semilinear bifurcation problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 1
SP - 191
EP - 207
AB - This note deals with the approximation, by a P1 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 H2. 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 H1 or L2-norms, we achieve optimal results.
LA - eng
KW - semilinear problem; bifurcation; singularity; adaptive finite element method; numerical examples; error estimates
UR - http://eudml.org/doc/197470
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.