IMI-BAS BAS
 

BulDML at Institute of Mathematics and Informatics >
IMI >
IMI Periodicals >
Serdica Mathematical Journal >
2000 >
Volume 26 Number 1 >

Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/405

Title: On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems
Authors: De Schepper, H.
Keywords: Finite Element Methods
Eigenvalue Problems
Periodic Boundary Conditions
Issue Date: 2000
Publisher: Institute of Mathematics and Informatics
Citation: Serdica Mathematical Journal, Vol. 26, No 1, (2000), 33p-48p
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.
URI: http://hdl.handle.net/10525/405
ISSN: 1310-6600
Appears in Collections:Volume 26 Number 1

Files in This Item:

File Description SizeFormat
sjm-vol26-num1-2000-p33-p48.pdf511.28 kBAdobe PDFView/Open

 



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

 

Valid XHTML 1.0!   Creative Commons License DSpace Software Copyright © 2002-2009  The DSpace Foundation - Feedback