Steklov特征值问题自适应间断有限元方法.pdf

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摘要··················································································3

ABSTRACT········································································4

1绪论·······················································································1

2预备知识················································································4

2.1基础知识·····································································4

2.2先验误差估计分析·······················································15

3自适应方法············································································20

3.1后验误差估计分析·······················································20

3.2自适应算法··································································34

4数值实验················································································35

总结··················································································39

参考文献···················································································40

致谢··················································································43

攻读硕士学位期间主要研究成果················································44

贵州师范大学学位论文原创性声明············································45

贵州师范大学学位论文使用授权书············································46

摘要

本文提出了求解二阶Steklov特征值问题的自适应间断有限元

方法。首先，引入了适当的分片Sobolev空间，利用格林公式推导

了Steklov特征值问题的间断有限元离散格式，导出了Galerkin正交

性，并完成了先验误差估计。其次，通过提升算子和构造辅助泡泡

函数，给出了后验误差指示子并证明了它的有效性和可靠性。最后，

我们在L型区域和方形区域上完成了数值实验，数值实验结果表明了

方案的有效性和理论结果的正确性。

关键词：Steklov特征值问题,自适应方法,间断有

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