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

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.