# Approximation of solution branches for semilinear bifurcation problems

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topCherfils, 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 -

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