GALERKIN SPECTRAL METHOD FOR HIGHER-ORDER BOUNDARY VALUE PROBLEMS ARISING IN THERMAL CONVECTION

TitleGALERKIN SPECTRAL METHOD FOR HIGHER-ORDER BOUNDARY VALUE PROBLEMS ARISING IN THERMAL CONVECTION
Publication TypeJournal Article
Year of Publication2002
AuthorsPapanicolaou N., Christov C.
JournalAnnuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique
Volume94
Pagination71-83
ISSN0205-0808
Keywordsbeam functions, natural convection, spectral methods
Abstract

In the present work we develop a Galerkin spectral technique for solving coupled higher-order boundary value problems arising in continuum mechanics. The set of so-called beam functions are used as a basis together with the harmonic functions. As featuring examples we solve two fourth-order boundary value problems related to the convective flow of viscous liquid in a vertical slot and a coupled convective problem. We show that the rate of convergence of the series is fifth-order algebraic both for linear and nonlinear problems of fourth order. The coupled problem exhibits fourth- and fifth-order convergence for the different unknown functions. Though algebraic, the fourth order rate of convergence is fully adequate for the generic problems under consideration, which makes the new technique a useful tool in numerical approaches to convective problems.

2000 MSC

37L65, 74S25, 76M22, 76E06, 76R10

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