Some results in lumped mass finite-element approximation of eigenvalue problems using numerical quadrature formulas
- Author
- AB Andreev, VA Kascieva and Michèle Vanmaele (UGent)
- Organization
- Abstract
- 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 degree k.
- Keywords
- LUMPED MASS FEM, EIGENVALUE PROBLEM, NUMERICAL INTEGRATION
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-200362
- MLA
- Andreev, AB, et al. “Some Results in Lumped Mass Finite-Element Approximation of Eigenvalue Problems Using Numerical Quadrature Formulas.” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol. 43, no. 3, 1992, pp. 291–311, doi:10.1016/0377-0427(92)90016-Q.
- APA
- Andreev, A., Kascieva, V., & Vanmaele, M. (1992). Some results in lumped mass finite-element approximation of eigenvalue problems using numerical quadrature formulas. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 43(3), 291–311. https://doi.org/10.1016/0377-0427(92)90016-Q
- Chicago author-date
- Andreev, AB, VA Kascieva, and Michèle Vanmaele. 1992. “Some Results in Lumped Mass Finite-Element Approximation of Eigenvalue Problems Using Numerical Quadrature Formulas.” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 43 (3): 291–311. https://doi.org/10.1016/0377-0427(92)90016-Q.
- Chicago author-date (all authors)
- Andreev, AB, VA Kascieva, and Michèle Vanmaele. 1992. “Some Results in Lumped Mass Finite-Element Approximation of Eigenvalue Problems Using Numerical Quadrature Formulas.” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 43 (3): 291–311. doi:10.1016/0377-0427(92)90016-Q.
- Vancouver
- 1.Andreev A, Kascieva V, Vanmaele M. Some results in lumped mass finite-element approximation of eigenvalue problems using numerical quadrature formulas. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 1992;43(3):291–311.
- IEEE
- [1]A. Andreev, V. Kascieva, and M. Vanmaele, “Some results in lumped mass finite-element approximation of eigenvalue problems using numerical quadrature formulas,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol. 43, no. 3, pp. 291–311, 1992.
@article{200362,
abstract = {{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 degree k.}},
author = {{Andreev, AB and Kascieva, VA and Vanmaele, Michèle}},
issn = {{0377-0427}},
journal = {{JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}},
keywords = {{LUMPED MASS FEM,EIGENVALUE PROBLEM,NUMERICAL INTEGRATION}},
language = {{eng}},
number = {{3}},
pages = {{291--311}},
title = {{Some results in lumped mass finite-element approximation of eigenvalue problems using numerical quadrature formulas}},
url = {{http://doi.org/10.1016/0377-0427(92)90016-Q}},
volume = {{43}},
year = {{1992}},
}
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