# On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems

Serdica Mathematical Journal (2000)

- Volume: 26, Issue: 1, page 33-48
- ISSN: 1310-6600

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topDe Schepper, H.. "On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems." Serdica Mathematical Journal 26.1 (2000): 33-48. <http://eudml.org/doc/11478>.

@article{DeSchepper2000,

abstract = {We deal with a class of elliptic eigenvalue problems (EVPs)
on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions
(BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational
formulation which is shown to fit into the general framework of abstract
EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert
spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs)
without and with numerical quadrature. The aim of the paper is to show
that well–known error estimates, established for the finite element approximation
of elliptic EVPs with classical BCs, hold for the present types of
EVPs too. Some attention is also paid to the computational aspects of the
resulting algebraic EVP. Finally, the analysis is illustrated by two non-trivial
numerical examples, the exact eigenpairs of which can be determined.},

author = {De Schepper, H.},

journal = {Serdica Mathematical Journal},

keywords = {Finite Element Methods; Eigenvalue Problems; Periodic Boundary Conditions; finite elements method; eigenvalue problem; periodic boundary conditions},

language = {eng},

number = {1},

pages = {33-48},

publisher = {Institute of Mathematics and Informatics},

title = {On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems},

url = {http://eudml.org/doc/11478},

volume = {26},

year = {2000},

}

TY - JOUR

AU - De Schepper, H.

TI - On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems

JO - Serdica Mathematical Journal

PY - 2000

PB - Institute of Mathematics and Informatics

VL - 26

IS - 1

SP - 33

EP - 48

AB - We deal with a class of elliptic eigenvalue problems (EVPs)
on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions
(BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational
formulation which is shown to fit into the general framework of abstract
EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert
spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs)
without and with numerical quadrature. The aim of the paper is to show
that well–known error estimates, established for the finite element approximation
of elliptic EVPs with classical BCs, hold for the present types of
EVPs too. Some attention is also paid to the computational aspects of the
resulting algebraic EVP. Finally, the analysis is illustrated by two non-trivial
numerical examples, the exact eigenpairs of which can be determined.

LA - eng

KW - Finite Element Methods; Eigenvalue Problems; Periodic Boundary Conditions; finite elements method; eigenvalue problem; periodic boundary conditions

UR - http://eudml.org/doc/11478

ER -

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