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A comparison of Galerkin and least squares finite element methods for nonlinear heat conduction in laminated composites

Book ·
OSTI ID:376014
 [1];  [2]
  1. Univ. of Kansas, Lawrence, KS (United States). Dept. of Mechanical Engineering
  2. Computational Research and Software Inc., Lawrence, KKS (United States)

This paper presents a comparison of p-version Galerkin and sp-version least squares finite element methods for non-linear heat conduction in laminated composites. Steady state heat conduction with temperature dependent thermal conductivities, internal heat generation, film coefficients and radiation parameters considered here is described by a non-linear elliptic equation. Galerkin method possesses the best approximation property for such problems. On the other hand, the least squares finite element method is ideally suited for non-linear problems regardless of the nature of equations and the nature of the nonlinearities. In this paper the authors investigate the competitiveness of the p-version least square finite element formulation (LSFEF) and p-version Galerkin method for non-linear heat conduction described by the non-linear elliptic equation. Two dimensional axisymmetric heat conduction in laminated composites is used as a sample problem. The discretized non-linear equations of equilibrium resulting from Galerkin method and the non-linear conditions resulting from the least squares method are solved and satisfied using Newton`s method and Newton`s method with line search. Numerical examples are presented for steady state heat conduction in laminated composites to compare the two methods for accuracy, efficiency, and convergence rates.

OSTI ID:
376014
Report Number(s):
CONF-960154--; ISBN 0-9648731-8-4
Country of Publication:
United States
Language:
English