ERROR ANALYSIS FOR FINITE-ELEMENT METHODS FOR STEADY NATURAL-CONVECTION PROBLEMS

被引：96

作者：

BOLAND, J ^{[1
]}

LAYTON, W ^{[1
]}

机构：

[1] UNIV PITTSBURGH,INST COMPUTAT MATH & APPLICAT,DEPT MATH & STAT,PITTSBURGH,PA 15260

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 1990年 / 11卷 / 5-6期

基金：

美国国家科学基金会;

关键词：

conducting walls; finite element; free convection; methods; Natural convection in enclosures;

D O I：

10.1080/01630569008816383

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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 (u,p,T), which we also establish. © 1990, Taylor & Francis Group, LLC. All rights reserved.

引用

页码：449 / 483

页数：35