On efficient least-squares finite element methods for convection-dominated problems

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/27955

Title:	On efficient least-squares finite element methods for convection-dominated problems
Authors:	Hsieh,PW;Yang,SY
Contributors:	數學研究所
Keywords:	RESIDUAL-FREE BUBBLES;PARTIAL-DIFFERENTIAL-EQUATIONS;ADVECTIVE-DIFFUSIVE EQUATIONS;STOKES EQUATIONS;ERROR ANALYSIS;FORMULATION
Date:	2009
Issue Date:	2010-06-29 19:38:49 (UTC+8)
Publisher:	中央大學
Abstract:	This paper focuses on the least-squares finite element method and its three variants for obtaining efficient numerical solutions to convection-dominated convection-diffusion problems. The coercivity estimates for the corresponding homogeneous least-squares energy functionals are derived, and based on which error estimates are established. One of the common advantages of these least-squares methods is that the resulting linear system is symmetric and positive definite. Numerical experiments that demonstrate the theoretical analysis of the developed methods are presented. It was observed that the primitive least-squares method performs poorly for convection-dominated problems while the stabilized, streamline diffusion and negatively stabilized streamline diffusion least-squares methods perform considerably better for interior layer problems, and the negatively stabilized streamline diffusion least-squares method is able to better capture the boundary layer behavior when compared with other least-squares methods. But all the least-squares methods do not give reasonable results for problem possessing both interior and boundary layer structures in the solution. (C) 2009 Elsevier B.V. All rights reserved.
Relation:	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Appears in Collections:	[Graduate Institute of Mathematics] journal & Dissertation

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