ALGORITHMS AND VISUALIZATION FOR SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS, PART II: DIRICHLET, NEUMANN AND ROBIN BOUNDARY CONDITIONS AND PROBLEMS IN 3D
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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.
author list (cited authors)
CHEN, G., NI, W., PERRONNET, A., & ZHOU, J.