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An analysis of the finite element method for natural convection problems
Author(s) -
Boland J.,
Layton W.
Publication year - 1990
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690060202
Subject(s) - finite element method , mathematics , natural convection , mixed finite element method , extended finite element method , thermal conduction , focus (optics) , mathematical analysis , stability (learning theory) , convection , mechanics , physics , thermodynamics , computer science , machine learning , optics
We derive stability properties and error estimates for the finite element method when used to approximate heat flow in a fluid enclosed by a solid medium. The coupled Navier Stokes system involves the Boussinesq equations in the fluid‐filled cavity linked through an interface with heat conduction in the solid enclosing the fluid. As we assume no extra regularity then can be shown to hold under mild restriction on the data (at least over a small time interval in R 3 ), we focus primarily on low order finite element spaces.