Algorithms and visualization for solutions of nonlinear elliptic equations, part II: Dirichlet, neumann and robin boundary conditions and problems in 3D

Goong Chen, Wei Ming Ni, Alain Perronnet, Jianxin Zhou

Research output: Contribution to journalReview articlepeer-review

2 Scopus citations

Abstract

This paper is a continuation of our earlier work [Chen et al., 2000]. Here, we use finite elements to help discretize a three-dimensional dumbbell-shaped domain with a cavity. The domain is thus nonconvex, nonstar-shaped, nonsymmetric and multiconnected. The finite element method is coupled with the scaling iterative algorithm to compute solutions of the Lane - Emden type equation with a single superlinear power nonlinearity term. The main thrust of this paper is to present graphical results (in color) for visualization in 3D to understand certain nonlinear effects and the occurrence of multiplicity of solutions when the domain has irregular geometry.

Original languageEnglish (US)
Pages (from-to)1781-1799
Number of pages19
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume11
Issue number7
DOIs
StatePublished - Jul 2001

Bibliographical note

Funding Information:
∗Supported in part by Texas A&M University Interdisciplinary Research Initiative IRI 99-22. E-mail: gchen@math.tamu.edu ySupported in part by NSF Grant DMS 9988635. E-mail: ni@math.umn.edu zE-mail: perronnet@ann.jussieu.fr xSupported in part by Texas A&M University Interdisciplinary Research Initiative IRI 99-68. E-mail: jzhou@math.tamu.edu

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