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Numerical experiments using hierarchical finite element method for nonlinear heat conduction in plates. (English) Zbl 1148.65077

Summary: We consider a nonlinear hierarchical finite element method for heat conduction problems over two- or three-dimensional plates. Problems considered are nonlinear because the heat conductivity parameter depends upon the temperature itself. This paper explores a new technique recently proposed by the first author which transforms a nonlinear parabolic problem to a linear problem at the discrete level. We present several numerical examples which demonstrate the efficiency of the current technique.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
80A20 Heat and mass transfer, heat flow (MSC2010)
80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
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