Isoparametric finite-element approximation of a Steklov eigenvalue problem
Isoparametric finite-element approximation of a Steklov eigenvalue problem
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DOI：
10.1093/imanum/24.2.309
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发表时间：
2004-04
影响因子：
2.1
通讯作者：
A. Andreev;T. Todorov
中科院分区：
文献类型：
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作者：
A. Andreev;T. Todorov
我们研究了二阶自伴椭圆型微分算子的Steklov特征值问题的有限元方法（FEM）的等参变量近似。本征函数和本征值的误差估计。我们证明了相同的估计的特征值的情况下，协调有限元提供的域的边界是很好的近似。从FE等参离散的Steklov问题的算法方面进行了分析。我们完成本文的数值结果证实了所考虑的理论。
We study the isoparametric variant of the finite-element method (FEM) for an approximation of Steklov eigenvalue problems for second-order, selfadjoint, elliptic differential operators. Error estimates for eigenfunctions and eigenvalues are derived. We prove the same estimate for eigenvalues as that obtained in the case of conforming finite elements provided that the boundary of the domain is well approximated. Some algorithmic aspects arising from the FE isoparametric discretization of the Steklov problems are analysed. We finish this paper with numerical results confirming the considered theory.