A bubble-stabilized least-squares finite element method for steady MHD duct flow problems at high Hartmann numbers

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题名:	A bubble-stabilized least-squares finite element method for steady MHD duct flow problems at high Hartmann numbers
作者:	Hsieh,PW;Yang,SY
贡献者:	數學研究所
关键词:	ADVECTION-DIFFUSION PROBLEMS;RESIDUAL-FREE BUBBLES;ELLIPTIC PROBLEMS;STOKES EQUATIONS;ERROR ANALYSIS;APPROXIMATION;FORMULATION;MULTISCALE
日期:	2009
上传时间:	2010-06-29 19:38:20 (UTC+8)
出版者:	中央大學
摘要:	In this paper we devise a stabilized least-squares finite element method using the residual-free bubbles for solving the governing equations of steady magnetohydrodynamic duct flow. We convert the original system of second-order partial differential equations into a first-order system formulation by introducing two additional variables. Then the least-squares finite element method using CO linear elements enriched with the residual-free bubble functions for all unknowns is applied to obtain approximations to the first-order system. The most advantageous features of this approach are that the resulting linear system is symmetric and positive definite, and it is capable of resolving high gradients near the layer regions without refining the mesh. Thus, this approach is possible to obtain approximations consistent with the physical configuration of the problem even for high values of the Hartmann number. Before incoorperating the bubble functions into the global problem, we apply the Galerkin least-squares method to approximate the bubble functions that are exact solutions of the corresponding local problems on elements. Therefore, we indeed introduce a two-level finite element method consisting of a mesh for discretization and a submesh for approximating the computations of the residual-free bubble functions. Numerical results confirming theoretical findings are presented for several examples including the Shercliff problem. (C) 2009 Elsevier Inc. All rights reserved.
關聯:	JOURNAL OF COMPUTATIONAL PHYSICS
显示于类别:	[數學研究所] 期刊論文

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