1. (海報論文：一般組或博士生組或碩士生組或大專生組)
National Chung Hsing University, Taichung, Taiwan, May 28-29, 2016
第5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或大專生組)
A novel least-squares finite element method for
solving convection-dominated problems
Xxx-Xxx Hsieh (謝XX), Department of Mathematics, National Central University, Taiwan
Advisor: Prof. Xxx-Xxx Yang (楊XX)
Abstract
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Problem description
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Results and discussion
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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
[2] A. Cangiani and E. Suli, Enhanced RFB method, Numer. Math., 101 (2005), pp
[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
[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
[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