周期复合材料振荡系数双曲问题的Galerkin多尺度有限元方法  

Galerkin Multiscale Finite Element Method for Periodic Composite Materials Hyperbolic Problems with Oscillating Coefficients

作　　者：孙艳萍[1] 宋士仓[2] 

机构地区：[1]河南工程学院数理科学系,河南郑州451191 [2]郑州大学数学系,河南郑州450052

出　　处：《河南工程学院学报（自然科学版）》2010年第3期54-60,共7页Journal of Henan University of Engineering：Natural Science Edition

摘　　要：通过双曲微分算子的局部解构造一组多尺度有限元基,利用这组多尺度有限元基构造出合适的多尺度有限元空间,然后利用Galerkin有限元方法求解周期复合材料振荡系数双曲问题,并分析了它的半离散多尺度有限元解的收敛性.In this paper,a Galerkin multiscale finite element method for solving periodic composite materials hyperbolic problems with oscillating coefficients is provided.And a numerical method is designed which is capable of correctly capture the large scale components of the solution on a coarse grid without accurately resolving all the small scale features in the solution.This is accomplished by incorporating the local microstructures of the differential operator into the finite element base functions.As a consequence,the base functions are adapted to the local properties of the differential operator.And the method is provided about the convergence analysis for Galerkin semi-discrete multiscale finite element solutions.

关 键 词：周期复合材料 振荡系数 双曲问题 Galerkin多尺度有限元方法 

分 类 号：O242.2[理学—计算数学]