Nonlinear One-Dimensional Problems

Prem K. Kythe and Dongming Wei
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Prem K. Kythe: University of New Orleans, Department of Mathematics
Dongming Wei: University of New Orleans, Department of Mathematics

Chapter 10 in An Introduction to Linear and Nonlinear Finite Element Analysis, 2004, pp 241-268 from Springer

Abstract: Abstract The mathematical models considered in this chapter involve only a single nonlinear differential equation with one unknown, which is one-dimensional in the space variable. These equations are encountered mostly in problems of radiation heat transfer, stress in plastics bars, non-Newtonian fluid flows between parallel plates, and turbulent flows in tubes. We introduce the standard Newton’ method, the method of steepest descent, and some nonlinear conjugate gradient methods for numerical solutions of the corresponding finite element nonlinear problems. Both Galerkin and Rayleigh-Ritz finite element methods are used to drive the finitedimensional finite element equations from nonlinear differential equations and their respective boundary conditions in idealized situations. For simplicity, only linear elements are used in the finite element methods.

Keywords: Steep Descent; Couette Flow; Linear Element; Linear Finite Element; Gray Body (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8160-9_10

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DOI: 10.1007/978-0-8176-8160-9_10

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