This article is cited in 12 papers

Error estimates for the Galerkin method as applied to time-dependent equations

P. V. Vinogradova, A. G. Zarubin

Far Eastern State Transport University, ul. Serysheva 47, Khabarovsk, 680021, Russia

Abstract: A projection method is studied as applied to the Cauchy problem for an operator-differential equation with a non-self-adjoint operator. The operator is assumed to be sufficiently smooth. The linear spans of eigenelements of a self-adjoint operator are used as projection subspaces. New asymptotic estimates for the convergence rate of approximate solutions and their derivatives are obtained. The method is applied to initial-boundary value problems for parabolic equations.

Key words: Galerkin method, operator equation, Hilbert space, Cauchy problem, convergence rate, orthoprojector, parabolic equations.

UDC: 519.63

Received: 06.10.2008
Revised: 12.01.2009

 English version: Computational Mathematics and Mathematical Physics, 2009, 49:9, 1567–1575

Bibliographic databases:

• 
• 
• 
• 
•