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標題: 圓盤上 Poisson 方程近似值的誤差估計
The error estimate for approximation of Poisson equation on a disk
作者: 簡正傑
Chien, Cheng-Chieh
關鍵字: error estimate
Poisson equation
出版社: 應用數學系所
引用: [1] A. D. Aleksandrov, Uniqueness conditions and estimates for the solution of the Dirichlet problem, Vestnil Leningrad. Univ. 18 (1963), no. 3, 5-29; English transl, Amer. Math. Soc. Transl. (2) 68 (1968), 89-119. [2] J. Ya. Bakel'' man, Theory of quasilinear elliptic equations, Sibirsk. Mat. Zn. 2 (1961), 179-186. [3] A. Bayliss, M. Gunzburger and E. Turkel, Boundary conditions for the numerical solution of elliptic equations in exterior regions, SIAM J. Appl. Math. vol 42, No 2, 430-451, (1982). [4] D.Gilbarg and N.S.Trudinger, Elliptic partial differential equations of second order, 2nd ed., Springer-Verlag, Berlin, Heidelberg, New York, and Tokyo, 1983. [5] H. J. Kuo abd N.S.Trudinger, Linear elliptic difference inequalities with randon coefficients, Math Comp. 55(1990), 37-53. [6] H. J. Kuo abd N.S.Trudinger, Positive difference operators on general meshes, Duke Mathematical Journal, vol. 83(1996), 415-433. [7] M. C. Lai, A note on finite difference discretizations for Poisson equation on a disk, Numerical Methods for Partial Differential Equations, vol 17, issue 3, 199-203, (2001). [8] M. C. Lai, Z. Li and X. Lin, Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain, Journal of Computational and Applied Mathematics , vol 191, 106-125, (2006). [9] R. Dautray and J.-L. Lions. Mathematical analysis and numerical methods for science and technology. vol. 1, 264 265, Springer-Verlag, Berlin, (1988).
摘要: 這篇論文的主要目的在於建立圓盤上Poisson方程的離散型極大值原理。我們從極大值原理繼續建立期望區域的收斂速度,然後得到圓盤上 Poisson 方程近似值的誤差估計。
The purpose of this work is devoted to establishing the discrete maximum principle for discrete Poisson equation on a polar disk. We proceed from the maximum principle to establish the desired bound of convergence rate. The error estimate for approximation of Poisson equation on a disk is then established.
其他識別: U0005-1707200810402000
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