Two-Order and Two-Scale Computation Method for Nonselfadjoint Elliptic Problems With Rapidly Oscillatory Coefficients
-
摘要: 为了求解具有迅速振荡系数的非自共轭椭圆问题,考虑了非自共轭椭圆问题二阶双尺度近似解的表示式,推导了二阶双尺度近似解的误差估计式,数值试验结果表明给出的近似解是有效的.
-
关键词:
- 非自共轭椭圆问题 /
- 迅速振荡系数 /
- 二阶双尺度有限元方法
Abstract: The purpose was to solve nonselfadjoint elliptic problems with rapidly oscillatory coefficients.A two-order and two-scale approximate solution expression for nonselfadjoint elliptic problems was considered,and the error estimation of the two-order and two-scale approximate solution was derived.The numerical result shows that the approximation solution is effective. -
[1] Bensoussan A,Lions J,Papanicolaou G.Asymptotic Analysis for Periodic Structures[M].Amsterdam:Nortth-Holland,1978. [2] Hornung U.Homogenization and Porous Media[M].New York:Springer-Verlag,1997. [3] Oleinik O A,Shamaev A S,Yosifian G A.Mathematical Problems in Elasticity and Homogenization[M].Amsterdam:North-Holland,1992. [4] Zhikov V V,Kozlov S M,Oleinik O A.Homogenization of Differential Operators and Internal Functionals[M].Berlin:Springer-Verlag,1994. [5] Bourget J F,Iria-Laboria.Numerical Experiments to the homogenization method for operators with periodic coefficients[J].Lecture Nots in Mathematics,1977,705:330-356. [6] Cioranescu D,Donato,P.An Introduction to Homogenization[M].Oxford:Oxford University Press,1999. [7] Cui J Z,Cao L Q.Two-scale asymptotic analysis methods for a class of elliptic boundary value problems with small periodic coefficients[J].Math Numer Sinica,1999,21(1):19-28. [8] Cao L Q,Cui J Z,Luo J L.Multiscale asymptotic expansion and a post-processing algorithm for second-order elliptic problems with highly oscillatory coefficients over general convex domains[J].J Comp Appl Math,2003,157(1):1-29. doi: 10.1016/S0377-0427(03)00372-8 [9] Cao L Q,Cui J Z.Finite element computation for elastic structures of composite materials formed by entirely basic configuration[J].J Num Math Appl,1998,20:25-37. [10] Cao L Q,Cui J Z,Zhu D C.Multiscale asymptotic analysis and numerical simulation for the second order Helmholtz with rapidly oscillating coefficients over general convex domains[J].SIAM J Numer Anal,2003,40(2):543-577. [11] Cao L Q,Cui J Z.Homogenization method for the quasi-periodic structures of composite materials[J].Math Num Sin,1999,21(3):331-344. [12] Feng Y P,Cui J Z.Multi-scale analysis and FE computation for the structure of composite materials with small periodic configurarion under condition of coupled thermoelasticity[J].Int J Numer Meth Engng,2004,60(11):1879-1910. doi: 10.1002/nme.1029 [13] Li Y Y,Cui J Z.Two-scale analysis method for predicting heat transfer performance of composite materials with random grain distribution[J].Sci Chi Ser A Math,2004,47(1):101-110. doi: 10.1360/04za0009 [14] Cui J Z,Yu X G.A two-scale method for identifying mechanical parameters of composite materials with periodic configuration[J].Acta Mech Sin,2006,22(6):581-594. doi: 10.1007/s10409-006-0037-2 [15] Yu X G,Cui J Z.The prediction on mechanical properties of 4-step braided composites via two-scale method[J].Compos Sci Tech,2007,67(3/4):471-480. doi: 10.1016/j.compscitech.2006.08.028 [16] Chen J R,Cui J Z.Two-scale finite element method for nonselfadjoint elliptic problems with rapidly oscillatory coefficients[J].Appl Math Comp,2004,150(2):585-601. doi: 10.1016/S0096-3003(03)00292-3 [17] Adams R A.Sobolev Space[M].New York:Academic Press,1975.
点击查看大图
计量
- 文章访问数: 1249
- HTML全文浏览量: 71
- PDF下载量: 704
- 被引次数: 0