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 language||English (US)|
|Number of pages||19|
|Journal||International Journal of Bifurcation and Chaos in Applied Sciences and Engineering|
|State||Published - Jul 2001|
Bibliographical noteFunding Information:
∗Supported in part by Texas A&M University Interdisciplinary Research Initiative IRI 99-22. E-mail: email@example.com ySupported in part by NSF Grant DMS 9988635. E-mail: firstname.lastname@example.org zE-mail: email@example.com xSupported in part by Texas A&M University Interdisciplinary Research Initiative IRI 99-68. E-mail: firstname.lastname@example.org