带齐次混合边界特征值问题的一种基于多尺度离散的有限元自适应算法.pdf

《带齐次混合边界特征值问题的一种基于多尺度离散的有限元自适应算法.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、学校代码:10663学号:4201210000330贵贵贵州州州师师师范范范大大大学学学硕硕硕士士士学学学位位位论论论文文文带带带齐齐齐次次次混混混合合合边边边界界界特特特征征征值值值问问问题题题的的的一一一种种种基基基于于于多多多尺尺尺度度度离离离散散散的的的有有有限限限元元元自自自适适适应应应算算算法法法Theadaptivefiniteelementmethodbasedonmulti-scalediscretizationsforeigenvalueproblemswithhomogeneousmixedboundaryconditions专业名称：计算数学专业代码：07010

2、2研究方向：有限元申请人姓名：陈星导师姓名：杨一都(教授)二零一五年三月二十日目录摘摘摘要要要······························································································IAbstract······························································································II1Introduction·····································

3、·················································12Preliminaries·····················································································33Aposteriorierrorestimateandadaptivefiniteelementalgorithmsbasedonmultiscalediscretizations·······················································

4、···········64Numericalexperiments······································································124.1Example····················································································12References·····················································································

5、······18Appendix·····························································································21Acknowledgements···············································································22DeclarationofOriginality································································

6、·····231摘要有限元自适应方法是科学和工程中数值求解偏微分方程基本而重要的数值工具之一。Babuska做了早期开拓性工作，继他之后，人们从理论上对有限元自适应方法做了大量广泛的工作，并在实际应用中取得成功。本文主要讨论了带齐次混合边界条件特征值问题有限元自适应算法。对基于Rayleigh商迭代的多尺度离散方案(见文SIAMJNumerAnal49(2011),pp.1602-1624中的方案3),我们给出了一个后验误差指示子，并且证明了该误差指示子的可靠性与有效性。另外，我们建立了两种相应的多尺度自适应算法。我们的算法在陈龙的软件包下用MATLAB编程运行，取得了理想的数值结果。

7、关关关键键键词词词:特征值问题,有限元，多尺度离散方案，后验误差,自适应算法.IAbstractAdaptivefiniteelementmethodsareafundamentalnumericalinstrumentinscienceandengineeringtosolvepartialdifferentialequations.Thesemethodshavebeenexten-sivelystudiedtheoreticallysin