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 - <p style="text-align: justify;">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.</p>