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

De 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 -