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標題: 利用裁縫有限點法解決擴散對流問題
A Modified Tailored Finite Point Method for Solving Convection-Diffusion-Reaction Problems
作者: 宋雅雯
Sung), Ya-Wen
關鍵字: Tailored Finite Point Method;裁縫有限點法;Convection-Diffusion-Reaction Problems;擴散對流問題
出版社: 應用數學系所
引用: [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, 1964. [2] H. Han, Z. Huang and R.B. Kellogg, The tailored finite point method and a problem of P. Hemker, Proceedings of the International Conference on Boundary and Interior Layers - Computational and Asymptotic Methods, Limerick, July 2008. [3] H. Han, Z. Huang and R.B. Kellogg, A tailored finite point method for a singular perturbation problem on an unbounded domain, J.Sci. Comp., 36 (2008), 243-261 [4] H. Han and Z. Huang, Tailored Finite point method for a singular perturbation problem with variable coefficients in two dimensions, J. Sci. Comp., 41(2009), pp. 200-220. [5] P.-W. Hsieh, Y.-T. Shih and S.-Y. Yang*, A tailored finite point method for steady MHD duct flow problems with boundary layers, Communications in Computational Physics (CiCP), 10 (2011), pp. 161- 182. [6] T.J.R. Hughes and A.N. Brooks, Streamline upwind Petrov-Galerkin formulations for convectiondominated flows with particular emphasis on the incompressible navier-stokes equations, Comput.Methods Appl. Mech. Engrg., 32 (1982), 199-259. [7] C. Johnson, A.H. Schatz and L.B. Wahlbin, Crosswind smear and pointwise errors in streamline diffusion finite element methods, Math. Comp., 49 (1987), 25-38. [8] G. Lube, An asymptotically fitted finite element method for convection dominated convection-diffusionreaction problems, Math. Mech. Comput., 72 (1992), 189-200. [9] Y. Shih and C. Chou, Tailored finite point methods for solving Poisson and biharmonic problems, the International Workshop on Physics and Mathematics (IWPM 2011), July 26-28, 2011. 19 [10] Y. Shih and H.C. Elman, Modified streamline difuusion schemes for convection-diffusion-reaction Problems, Computer Methods in Apppiled Mechanics and Engineering,174 (1999), 137-151. [11] Y. Shih and H.C. Elman, Iterative Methods for Stabilized Discrete convection-diffusion-reaction Problems, IMA, Numerical Analysis, 20(2000), 3, 333-385. [12] Y. Shih, R.B. Kellogg and Y. Chang, Characteristic tailored finite point method for convection-dominated convection-diffusion-reaction problems , J. Sci. Comp., 47(2010), pp. 198-215. [13] Y. Shih, R.B. Kellogg and P. Tsai, A Tailored Finite Point Method for convection-diffusion-reaction Problems , J. Sci. Comp., 43(2010), pp. 239-260. [14] M. Stynes and L. Tobiska, Necessary L2-uniform convergence conditions for difference schemes for two dimensional convection-diffusion-reaction problems, Computers Math. Applic., 29 (1998), 45-53. [15] T. Linβ, ”Layer-adapted meshes for reaction-convection-diffusion,” Springer-Verlag Berlin Heidelberg (2010) [16] T. Linβ, ” An upwind different scheme on a novel Shishkin-type mesh for a linear convection-diffusion problem, J. Comput. Appl. Math., 110 (1999), pp. 93-104. [17] T. Linβ, M. Stynes, Numerical methods on Shishkin meshes for linear convection-diffusion problems, Computers Math. Applic., 190 (2001), 3527-3542. [18] N. Kopteva, E. O'riordan, Shishkin meshesin the numerical solution of singularly perturbed differentail equations., J. Numerical analysis and modeling, Vol. 7, Num. 3, 393-415. 20

In the thesis,we propose a modified tailored finite point method for solving the convection-diffusionreaction
problems. In our numerical tests, our method exhibits high precision in resolving the internal and
boundary layers without mesh refinement or gridline aligned problems for small diffusion coefficient ε. We
depicts that modified tailored finite point method has excellent performance in comparing with original
tailored finite point method and upwind streamline finite element method when ε is small.
其他識別: U0005-2811201114411800
Appears in Collections:應用數學系所

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