两点边值问题有限元方法的程序实现与计算分析  

IMPLEMENTATION OF FINITE ELEMENT METHODS OF TWO- POINT BOUNDARY VALUE PROBLEMS AND PROGRAMMING

作　　者：高理平[1] 杨光[2] 

机构地区：[1]山东师范大学数学科学学院,济南250014 [2]同济大学土木工程学院,上海200092

出　　处：《山东师范大学学报（自然科学版）》2009年第1期1-5,共5页Journal of Shandong Normal University(Natural Science)

基　　金：山东省优秀中青年科学家科研奖励基金资助（2007BS01020）;山东省自然科学基金重大项目（Z2006A02）;山东省自然科学基金资助项目（Y2007A14Y2008A19）

摘　　要：以两点边值问题为模型，从程序实现和计算的角度讨论了该问题的有限元方法，着重给出了实现线性有限元方法的Fortran程序和Matlab程序，用表格和图形展示了有限元解和它们真解在L^2和H^1模下的误差和收敛阶，计算结果验证了理论分析．This paper aims at implementing the linear finite element method of the two- point value problem and giving Fortran and Matlab programs in detail. Functions, subroutines and how to post - process computational results such as calculating the error of the finite element solution in L^2 and H^1 norms are shown in the programs. Computational results such as error at some points, relative and absolute error as well as convergence orders in L^2 and H^1 norms are displayed in figures and tables and validate the theoretical analysis of the finite element method.

关 键 词：两点边值问题 有限元方法 收敛 误差 FORTRAN MATLAB 

分 类 号：O241.8[理学—计算数学]