[Back to Results | New Search]

Student Number 952201028 Author Shih-Chao Kao(高仕超) Author's Email Address 952201028@cc.ncu.edu.tw Statistics This thesis had been viewed 1549 times. Download 665 times. Department Mathematics Year 2007 Semester 2 Degree Master Type of Document Master's Thesis Language English Title Some Residual-Free Bubble Enrichment Least-Squares Finite Element Method for the Convection-Diffusion Equation Date of Defense 2008-06-26 Page Count 31 Keyword convection-diffusion equation finite element method least-squares residual-free bubble Abstract In this thesis, we formulate the least-squares finite element method using piececewise linears to solve the convection-diffusion equation which is convection-dominated and we find that the solution is diffusive and the classical mesh refinement for the least-squares finite element method is not an economical method. Then we use the

residual-free bubble method to enrich the least-squares finite element method. This is a new application of residual-free bubble method and we solve some test problems. The numerical results show that the residual-feee bubble method for the least-squares finite element method has a good effect of enrichment。Table of Content 中文摘要.................................................i

英文摘要................................................ii

致謝詞.................................................iii

目錄....................................................iv

圖目錄...................................................v

表目錄..................................................vi

1.Introduction...........................................2

2. The LSFEM for the convection-diffusion equation.......4

3. The LSFEM enriched by a residual-free bubble method...8

3.1. Analytical approach............................... 13

3.2. Numerical approach.................................15

4. Numerical results....................................16

5. Conclusion...........................................29

Reference...............................................29Reference [1] B.N. Jiang, and L.A. Povinelli, Least-Squares Finite element method for fluid dynamics, Comput. Methods. Appl. Mech. Engrg. 81 (1990) 13-37.

[2] F. Brezzi, M.O. Bristeau, L.P. Franca, M. Mallet, and G. Roge, A relationship between stabilized finite element methods and the Galerkin method with bubble functions,Comput. Methods Appl. Mech. Engrg. 96 (1992) 117-129.

[3] L.P. Franca, S.L. Frey, and T.J.R Hughes, Stabilized-finite element methods: I. Application to advective-diffusive model, Comput. Methods Appl. Mech. Engrg.

95 (1992) 253-276.

[4] F. Brezzi and A. Russo, Choosing bubbles for advection-diffusion problems,Math.Models Methods Appl., 4 (1994)

571-587.

[5] L.P. Franca, and F. Charbel, On the Limitations of Bubble Functions, Comput. Methods Appl. Mech. Engrg. 117 (1994) 225-230.

[6] L.P. Franca, and F. Charbel, Bubble functions prompt unusual stabilized finite element methods, Comput. Methods. Appl. Mech. Engrg. 123 (1995) 299-308.

[7] T.F. Chen, G.J. Fix, and H.D. Yang, Numerical Studies of Optimal Grid Construction, Numer. Methods Partial Different. Eq. 12 (1996) 191-206.

[8] L.P. Franca, and A. Russo , Mass lumping emanating from residual-free bubbles, Comput. Methods Appl. Mech. Engrg. 142 (1997) 353-360.

[9] F. Brezzi, L.P. Franca, A. Russo, Further considerations on the residual-free bubbles for advective-diffusive equations, Comput. Methods Appl. Mech. Engrg.

166 (1998) 25-33.

[10] B.N. Jiang, On the least-squares method, Comput. Methods Appl. Mech. Engrg. 152 (1998) 239-257

[11] J.M. Fiard, T.A. Manteu®el, and S.F. Mccormick, First-order sustem leasts squares (FOSLS) for convection-diffusion problems: numerical results, SIAM

J. Sci. Comput. 19 (1998) 1958-1979.

[12] L.P. Franca, A. Nesliturk and M. Stynes, On the stability of residual-free bubbles for convection-diffusion problems and their approximation by a two-level finite element method, Comput. Methods Appl. Mech. Engrg. 166 (1998) 35-49.

[13] L.P. Franca, and A.P. Macedo, A two-level finite element method and its application to Helmholtz equation, Int. J. Numer. Methods Engrg. 43 (1998) 23-42.

[14] P.B. Bochev, and J. Choi, A Comparative Study of Least-squares, SUPG and Galerkin Methods for Convection Problem, Int. J. Comput. Fluids 15 (2001)

127-146.

[15] L.P. Franca, and A. Nesliturk, On a two-level finite element method to the incompressible Navier-Stokes equations, Int. J. Numer. Meth. Engrg 52 (2001)

433-453.

[16] L.P. Franca, and F.N. Hwang, Refining the submesh strategy in the two-level finite element method: Application to the advection-diffusion equation, Int. J.

Numer. Meth. Fluids 39 (2002) 161-187.

[17] L.P. Franca LP, G. Hauke and A. Masud, Revisiting stabilized finite element methods for the advective-diffusive equation, Comput. Methods Appl. Mech. En-

grg. 195 (2006) 1560-1572.

[18] M. Parvazinia, V. Nassehi, and R.J Wakeman, Multi-scale finite element modelling using bubble function method for a convection-diffusion problem , Chem.

Engrg. Sci. 61 (2006) 2742-2751.

[19] A. Russo, Streamline-upwind Petrov/Galerkin method (SUPG) vs residual-free bubble (RFB), Comput. Methods Appl. Mech. Engrg. 195 (2006) 1608-1620.

[20] C. Johnson, Numerical Solution of Partial Differential Equation by the Finite

Element Method, Cambridge University Press, Cambridge, 1987.

[21] K.W Morton, Numerical Solution of Convection-Diffusion Problems, Chapman & Hall Press, 1996

[22] S.A. Berger, W. Goldsmith, and E.R. Lewis, Introduction to bioengineering, Ox-

ford University Press, 1996

[23] B.N. Jiang. The Least-Squares Finite Element Method, Springer-Verlag, Berlin, 1998

[24] D. Jean, and H. Antonio, Finite Element Methods for Flow Problems, John Wiley & Sons Inc Press, 2003.

[25] S.C. Breneer, and L.R. Scott, The Mathmatical Theory of Finite Element Method, Springer-Verlag, New-York, 1994.Advisor Feng-Nan Hwang(黃楓南)

Files approve immediately

952201028.pdf Date of Submission 2008-07-16

Our service phone is (03)422-7151 Ext. 57407,E-mail is also welcomed.