A novel least-squares finite element method forsolving convection-dominated problems

A novel least-squares finite element method forsolving convection-dominated problems

Xxx-Xxx Hsieh ( 謝 XX), Department of Mathematics, National Central University, Taiwan (xxxx@math.ncu.edu.tw)Advisor: Prof. Xxx-Xxx Yang ( 楊 XX)

National Dong Hwa University, Hualien, Taiwan, May 31-June 1, 2014

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 )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 )

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Results and discussion

Problem description

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ConclusionsWe 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

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