Some results in lumped mass finite-element approximation of eigenvalue problems using numerical quadrature formulas
Some results in lumped mass finite-element approximation of eigenvalue problems using numerical quadrature formulas
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DOI：
10.1016/0377-0427(92)90016-q
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发表时间：
1992-12
影响因子：
2.4
通讯作者：
A. Andreev;Va Kascieva;M. Vanmaele
中科院分区：
文献类型：
--
作者：
A. Andreev;Va Kascieva;M. Vanmaele
本文建立了用集中质量有限元逼近二阶椭圆型特征值问题的近似特征值和特征函数的收敛和收敛速度。Fix(1972)，Ishihara(1977)，Strang and Fix(1973)和童等人已经讨论了集中质量技术的各个方面。(1971)，以及其他。在我们的方法中，质量矩阵的集中是由于在度数的矩形拉格朗日有限元上使用Lobatto积分求积公式而导致的。
In this paper we establish the convergence and the rate of convergence for approximate eigenvalues and eigenfunctions of second-order elliptic eigenvalue problems, obtained by a lumped mass finite-element approximation. Various aspects of lumped mass techniques have been discussed for such eigenvalue problems by Fix (1972), Ishihara (1977), Strang and Fix (1973) and Tong et al. (1971), among others. In our approach the lumping of the mass matrix results from the use of a Lobatto quadrature formula for the integrals over rectangular Lagrange finite elements of degreek.