This article is cited in 2 papers

Study of convergence of the projection-difference method for hyperbolic equations

S. E. Zhelezovsky

Saratov State Socio-Economic University

Abstract: We consider the Cauchy problem for an abstract quasilinear hyperbolic equation with variable operator coefficients and a nonsmooth but Bochner integrable free term in a Hilbert space. Under study is the scheme for approximate solution of this problem which is a combination of the Galerkin scheme in space variables and the three-layer difference scheme with time weights. We establish an a priori energy error estimate without any special conditions on the projection subspaces. We give a concrete form of this estimate in the case when discretization in the space variables is carried out by the finite element method (for a partial differential equation) and by the Galerkin method in Mikhlin form.

Keywords: abstract hyperbolic equation, projection-difference method, Galerkin method, three-layer difference scheme, error estimate.

UDC: 517.988.8

Received: 15.06.2005
Revised: 15.03.2006

 English version: Siberian Mathematical Journal, 2007, 48:1, 76–83

Bibliographic databases:

• 
• 
• 
•