IJPAM: Volume 6, No. 4 (2003)

STABILITY AND CONVERGENCE FOR
DISCRETIZATION METHODS WITH
APPLICATIONS TO WAVELET
GALERKIN SCHEMES

Klaus Böhmer$^1$, Stephan Dahlke$^2$
FB12, Mathematics and Informatics
Philipps-University of Marburg
Hans-Meerwein Strasse, Lahnberge
D-35032 Marburg, GERMANY
$^1$e-mail: boehmer@mathematik.uni-marburg.de
$^2$e-mail: dahlke@mathematik.uni-marburg.de


Abstract.We give a simple approach for a well-known, but rather complicated theory for general discretization methods, Petryshyn [#!Petryshyn86!#] and Zeidler [#!Zeidler90!#]. We employ only some basic concepts such as invertibility, compact perturbation and approximation. It allows to treat a wide class of space discretization methods and operator equations. As demonstration examples we use wavelet Galerkin methods applied to saddle point problems, Navier-Stokes equations and to numerical bifurcation. This extends some recent results for wavelet methods, e.g., to numerical bifurcation.

Received: April 24, 2003

AMS Subject Classification: 65P30; 65N55

Key Words and Phrases: stability and convergence, Galerkin schemes, bordered systems, wavelets, elliptic, saddle point and Navier-Stokes problems

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 6
Issue: 4