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Dondlinger, Mireille; Margerit, Jonathan; Dauby, Pierre C.

Extended Galerkin-Eckhaus method in nonlinear thermoconvection. (English) Zbl 1134.80003

J. Non-Equilibrium Thermodyn. 32, No. 2, 155-179 (2007).
In this paper the authors extend the Galerkin-Eckhaus method in order to examine the behaviour of the free Rayleigh-Bénard and Marangoni-Bénard problems with heat-conducting boundaries. This extension consists in choosing appropriately the basis functions in which the unknowns are expanded. The main result of this paper establishes that in all thermoconvection problems, the Galerkin-Eckhaus method provides very good results, even for thresholds, provided the basis functions are appropriately chosen. Related results concerning the eigenfunctions of these operators are also established in the present paper.
Reviewer: Teodora-Liliana Rădulescu (Craiova)

Cited in 2 Documents

MSC:

80A20 Heat and mass transfer, heat flow (MSC2010)
76M10 Finite element methods applied to problems in fluid mechanics
76R10 Free convection
80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer

Keywords:

Galerkin-Eckhaus method; nonlinear thermoconvection; Rayleigh-Bénard problem
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References:

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