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Volume 22, Issue 4
The Lower Approximation of Eigenvalue by Lumped Mass Finite Element Method

Jun Hu, Yunqing Huang & Hongmei Shen

J. Comp. Math., 22 (2004), pp. 545-556.

Published online: 2004-08

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  • Abstract

In the present paper, we investigate properties of lumped mass finite element method (LFEM hereinafter) eigenvalues of elliptic problems. We propose an equivalent formulation of LFEM and prove that LFEM eigenvalues are smaller than the standard finite element method (SFEM hereinafter) eigenvalues. It is shown, for model eigenvalue problems with uniform meshes, that LFEM eigenvalues are not greater than exact solutions and that they are increasing functions of the number of elements of the triangulation, and numerical examples show that this result equally holds for general problems.

  • Keywords

Lumped mass, Eigenvalue, Min-max principle, Finite element.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-545, author = {Hu , JunHuang , Yunqing and Shen , Hongmei}, title = {The Lower Approximation of Eigenvalue by Lumped Mass Finite Element Method}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {4}, pages = {545--556}, abstract = {

In the present paper, we investigate properties of lumped mass finite element method (LFEM hereinafter) eigenvalues of elliptic problems. We propose an equivalent formulation of LFEM and prove that LFEM eigenvalues are smaller than the standard finite element method (SFEM hereinafter) eigenvalues. It is shown, for model eigenvalue problems with uniform meshes, that LFEM eigenvalues are not greater than exact solutions and that they are increasing functions of the number of elements of the triangulation, and numerical examples show that this result equally holds for general problems.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10304.html} }
TY - JOUR T1 - The Lower Approximation of Eigenvalue by Lumped Mass Finite Element Method AU - Hu , Jun AU - Huang , Yunqing AU - Shen , Hongmei JO - Journal of Computational Mathematics VL - 4 SP - 545 EP - 556 PY - 2004 DA - 2004/08 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10304.html KW - Lumped mass, Eigenvalue, Min-max principle, Finite element. AB -

In the present paper, we investigate properties of lumped mass finite element method (LFEM hereinafter) eigenvalues of elliptic problems. We propose an equivalent formulation of LFEM and prove that LFEM eigenvalues are smaller than the standard finite element method (SFEM hereinafter) eigenvalues. It is shown, for model eigenvalue problems with uniform meshes, that LFEM eigenvalues are not greater than exact solutions and that they are increasing functions of the number of elements of the triangulation, and numerical examples show that this result equally holds for general problems.

Hu , JunHuang , Yunqing and Shen , Hongmei. (2004). The Lower Approximation of Eigenvalue by Lumped Mass Finite Element Method. Journal of Computational Mathematics. 22 (4). 545-556. doi:
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