Error analysis for finite element methods for steady natural convection problems
作者:
J. Boland,
W. Layton,
期刊:
Numerical Functional Analysis and Optimization
(Taylor Available online 1990)
卷期:
Volume 11,
issue 5-6
页码: 449-483
ISSN:0163-0563
年代: 1990
DOI:10.1080/01630569008816383
出版商: Marcel Dekker, Inc.
关键词: AMS-MOS Numbers: primary 75R10;AMS-MOS Numbers: secondary 65M60;Natural convection in enclosures;free convection;finite element methods;conducting walls
数据来源: Taylor
摘要:
We analyze the error in finite element methods in approximating, so-called, free or natural convection problems. We also include the effects of conducting solid walls in our analysis. Under a uniqueness condition on the Rayleigh and Prandtl numbers (which we derive), we give direct, quasioptimal error estimates for “div-stable” finite element spaces for the fluid variables and general conforming finite element spaces for the temperature. At larger Rayleigh numbers, we give analogous, asymptotic error estimates, basing this analysis upon local uniqueness properties of the true solution (upT), which we also establish.
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