Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18090
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dc.contributor簡澄陞zh_TW
dc.contributorCheng-Sheng Chienen_US
dc.contributor楊肅煜zh_TW
dc.contributorSuh-Yuh Yangen_US
dc.contributor.advisor施因澤zh_TW
dc.contributor.advisorYin-Tzer Shihen_US
dc.contributor.author蔡佩珊zh_TW
dc.contributor.authorTsai, Pei-Shanen_US
dc.contributor.other中興大學zh_TW
dc.date2010zh_TW
dc.date.accessioned2014-06-06T07:02:51Z-
dc.date.available2014-06-06T07:02:51Z-
dc.identifierU0005-0906200912522700zh_TW
dc.identifier.citation[1] T.J.R. Hughes and A.N. Brooks, Streamline upwind Petrov-Galerkin formulations for convection-dominated flows with particular emphasis on the incompressible navier-stokes equations, Comput.Methods Appl. Mech. Engrg., 32 (1982), 199V259. [2] C. Johnson, A.H. Schatz and L.B. Wahlbin, Crosswing smear and pointwise errors in streamline diffusion finite element methods, Math. Comp., 49 (1987), 25-38. [3] Y. Shih and H.C. Elman, Modified streamline diffusion schemes for convectiondiffusion problems, Computer Methods in Applied Mechanics and Engineering, 174 (1999), 137-151. [4] H.G. Roos, M. Stynes and L. Tobiska, Numerical methods for singular perturbed differential equations, Springer-Verlag, New York, 1996. [5] 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. [6] 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. [7] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, 1964. [8] H. Han and Z. Huang, Tailored Finite point method for a singular perturbation problem with variable coefficients in two dimensions, J.Sci. Comp., 2009. [9] M. Stynes and L. Tobiska, Necessary L2-uniform convergence conditions for difference schemes for two dimensional convection-diffusion problems, Computers Math. Applic., 29 (1998), 45-53. [10] H. Eckhaus, Boundary layers in linear elliptic singular pertubation problems, SIAM Rev., 14 (1972), 225-270. [11] C. Johnson, U. N¨avert, An analysis of some finite element methods for advectiondiffusion problems.Analytical and Numerical Approaches to Asymptotic Problem in Analysis (O. Axelsson, L.S. Frank, A. ver der Sluis, eds.), North-Holland, Amsterdam, 1981.en_US
dc.identifier.urihttp://hdl.handle.net/11455/18090-
dc.description.abstract在這篇論文裡,我們研究裁縫有限點法來解擴散對流反應方程式。裁縫有限點法的解空間的基底函數是由指數函數、修正的貝塞耳函數及三角函數相乘所組成。在理論分析上我們可以求得裁縫有限點法在對流控制問題的數值截尾誤差為O(e^-Pe),這裡的Pe是一個網格貝克勒數。當擴散係數很小時,由我們的數值測試證明了在邊界層的誤差不管網格大小都會在機器誤差的精準之下,而內部層的誤差則在網格大小之下。這描述了在對流控制問題上,裁縫有限點法會有相當高的準確度。zh_TW
dc.description.abstractIn this thesis, we study a tailored finite point method (TFP) for solving the convection-diffusion-reaction equation. The basis functions of solution space of the TFP are composed from the product of an exponential function, modified Bessel functions and trigonometric functions. The numerical truncation error for the TFP is in the order of O(e^-Pe) for the convection dominated problem, where Pe is the mesh Péclet number. Our numerical tests show that for small diffusion coefficient the numerical boundary layer is under the machine precision regardless the mesh size, and the internal layer is also within the mesh size. This depicts that the TFP method has high accuracy for convection-dominated problem.en_US
dc.description.tableofcontents1 Introduction ........................................ 1 2 The Tailored Finite Point Methods......... 3 2.1Introduction....................................... 3 2.2 The five-point TFP scheme................. 5 2.3 The seven-point TFP scheme............. 8 2.4 The nine-point TFP scheme............... 11 3 Truncation Errors................................. 14 4 Numerical Experiments........................ 19 5 Conclusions........................................ 23 Bibliography........................................... 33en_US
dc.language.isoen_USzh_TW
dc.publisher應用數學系所zh_TW
dc.relation.urihttp://www.airitilibrary.com/Publication/alDetailedMesh1?DocID=U0005-0906200912522700en_US
dc.subjectTailored finite pointen_US
dc.subject裁縫有限點zh_TW
dc.subjectconvection-diffusion-reactionen_US
dc.subjectfinite elementen_US
dc.subjectboundary layeren_US
dc.subjectinternal layeren_US
dc.subject擴散對流反應zh_TW
dc.subject有限單元zh_TW
dc.subject邊界層zh_TW
dc.subject內部層zh_TW
dc.title利用裁縫有限點法來解擴散對流反應問題zh_TW
dc.titleA Tailored Finite Point Method for Convection-Diffusion-Reaction Problemsen_US
dc.typeThesis and Dissertationzh_TW
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