本論文共9頁(yè)，約7000字。
摘 要
基于多尺度空間, 提出了求偏微分方程的Galerkin多層修正迭代算
法. 并討論了迭代修正算法的收斂性. 提出的方案能容易地實(shí)現(xiàn) 時(shí)間
和空間方向的局部加密自適應(yīng)修正過(guò)程. 提供的數(shù)值例子說(shuō)明了方法
的有效性.

關(guān)鍵詞 偏微分方程, Galerkin方法, 迭代法, 自適應(yīng)方法.

參考文獻(xiàn):
[1] I. Daubechies, Ten lecture on wavelets, Regional Conference Series in
Applied Mathematics[M], 1992, vol. 61, SIAM, Phliadelpha.
[2] Beylkin G. On the Representation od Operators in Bases od Compactly
Supported Wavelets[J]. SIAM J. Numer. Anal., 1992, 6, pp.1716-1740.
[3] S. Qian and J. Weiss, Wavelets and the Numerical solution of partial
di®erential equations[J], Journal of Computational Physics, 1993, 106,
pp. 155-175.
[4] B. Alpert, G. Beylkin, D. Gines, and L. Vozovoi. Adaptive solution of
partial di®erential equations in multiwavelet bases[J]. Journal of Com-
putational Physics, 2002, v. 182, pp. 149-190.
[5] B. Cockburn, and C. Shu, The local discontinuous Galerkin method for
time-depended convection-di®usion systems[J], SIAM J. Numer. Anal.,
1998, 35(6), pp. 2440-2463.
[6] N. Chevaugeon, J. Xin, P. Hu, X. Li, D. Cler, J.E. Flaherty and M.S.
Shephard. Discontinuous Galerkin Methods Applied to Shock and Blast
Problems[J]. Journal of Scienti¯c Computing , 2005, vol.2 PP.227-243.
[7] Z. Chen, C. A. Micchelli, and Y. Xu, A multilevel method for solving
operator equations[J], J. Math. Appl., 2002, 262 688-699.
[8] W. Fang, F. Ma and Y. Xu, Multilevel iteration methods for solving
intergral equations of second kind[J], J. Integral Equations Appl., 2002,
14, 355-376.