The combined effect of numerical integration and
approximation of the boundary in the finite element method
for eigenvalue problems |
| |
Authors: | Michèle Vanmaele Alexander Ženíšek |
| |
Institution: | (1) Department of Math. Analysis, University Gent, Galglaan 2, 9000 Gent, Belgium, e-mail: mv@cage.rug.ac.be , BE;(2) Department of Mathematics, Technical University, Technická 2, 61669 Brno, Czech Republic, e-mail: zenisek@kinf.fme.vutbr.cz , CS |
| |
Abstract: | Summary.
The paper deals with the finite element analysis of second
order elliptic eigenvalue problems when the approximate domains
are not subdomains of the original domain
and when at the same time numerical integration is used for computing the
involved bilinear forms. The considerations are restricted to piecewise
linear approximations. The optimum rate of convergence
for approximate
eigenvalues is obtained provided that a quadrature formula of first
degree of precision is used. In the case of a simple exact eigenvalue
the optimum rate of convergence
for approximate eigenfunctions in the
-norm is proved while in the
-norm an
almost optimum rate of convergence (i.e. near to
is achieved. In both
cases a quadrature formula of first degree of precision is used.
Quadrature formulas with degree of precision equal to zero are also
analyzed and in the case when the exact eigenfunctions belong only to
the convergence
without the rate of convergence is proved. In the case of
a multiple exact eigenvalue the approximate eigenfunctions are compard
(in contrast to standard considerations) with linear combinations of
exact eigenfunctions with coefficients not depending on the mesh
parameter .
Received September 18, 1993 / Revised
version received September 26, 1994 |
| |
Keywords: | Mathematics Subject Classification (1991):65N30 65N25 |
本文献已被 SpringerLink 等数据库收录! |
|