Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

De Schepper, H.. "Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem." Serdica Mathematical Journal 25.2 (1999): 177-184. <http://eudml.org/doc/11512>.

@article{DeSchepper1999,
abstract = {We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].},
author = {De Schepper, H.},
journal = {Serdica Mathematical Journal},
keywords = {Eigenvalue Problems; Periodic Boundary Conditions; Circulant Matrices; eigenvalue problem; periodic boundary conditions; circulant matrices; consistent mass finite element method; error estimates},
language = {eng},
number = {2},
pages = {177-184},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem},
url = {http://eudml.org/doc/11512},
volume = {25},
year = {1999},
}

TY - JOUR
AU - De Schepper, H.
TI - Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem
JO - Serdica Mathematical Journal
PY - 1999
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 25
IS - 2
SP - 177
EP - 184
AB - We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].
LA - eng
KW - Eigenvalue Problems; Periodic Boundary Conditions; Circulant Matrices; eigenvalue problem; periodic boundary conditions; circulant matrices; consistent mass finite element method; error estimates
UR - http://eudml.org/doc/11512
ER -