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

Serdica Mathematical Journal (1999)

- Volume: 25, Issue: 2, page 177-184
- ISSN: 1310-6600

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topDe 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 -

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