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A novel least-squares finite element method for solving convection-dominated problems

National Dong Hwa University , Hualien, Taiwan, May 31-June 1, 2014. A novel least-squares finite element method for solving convection-dominated problems. Xxx-Xxx Hsieh ( 謝 XX ), Department of Mathematics, National Central University, Taiwan ( xxxx@math.ncu.edu.tw )

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A novel least-squares finite element method for solving convection-dominated problems

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  1. National Dong Hwa University, Hualien, Taiwan, May 31-June 1, 2014 A novel least-squares finite element method for solving convection-dominated problems Xxx-XxxHsieh (謝XX), Department of Mathematics, National Central University, Taiwan (xxxx@math.ncu.edu.tw) Advisor:Prof. Xxx-Xxx Yang(楊XX) 第2屆台灣工業與應用數學會年會 (海報論文:一般組或博士生組或碩士生組) Abstract Please insert the abstract here! Problem description Please insert the problem description and background here! Results and discussion Insert your text here! Conclusions We have proposed a novel LSFEM using continuous piecewise linear elements enriched with residual-free bubbles. This enriched LSFEM not only inherits the advantages of the primitive LSFEM but also exhibits the characteristics of the residual-free bubble method. Through a series of numerical experiments, the enriched LSFEM certainly demonstrates a superior performance over the primitive LSFEMs for solving convection-dominated problems. The above results have been generalized to the system of convection-dominated equations such as the steady MHD duct flows with a high Hartmann number. References [1] F. Brezzi and A. Russo, Choosing bubbles for advection-diffusion problems, Math. Models Meth. Appl. Sci., 4 (1994), pp. 571-587. [2] A. Cangiani and E. Suli, Enhanced RFB method, Numer. Math., 101 (2005), pp. 273-308. [3] L. P. Franca, S. L. Frey, and T. J. R. Hughes, Stabilized finite element methods: I. application to the AD model,Comput. Methods Appl. Mech. Engrg., 95 (1992), pp. 253-276. [4] L. P. Franca, J. V. A. Ramalho, and F. Valentin, Multiscale and residual-free bubble functions for RAD problems, Int. J. Multiscale Comput. Eng., 3 (2005), pp. 297- 312. [5] T. Y. Hou and X.-H. Wu, A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys., 134 (1997), pp. 169-189.

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