Siberian Mathematical Journal

, Volume 46, Issue 2, pp 293–304

On error estimates in the Galerkin method for hyperbolic equations

  • S. E. Zhelezovskii
Article

DOI: 10.1007/s11202-005-0030-1

Cite this article as:
Zhelezovskii, S.E. Sib Math J (2005) 46: 293. doi:10.1007/s11202-005-0030-1

Abstract

We consider the Cauchy problem in a Hilbert space for a second-order abstract quasilinear hyperbolic equation with variable operator coefficients and nonsmooth (but Bochner integrable) free term. For this problem, we establish an a priori energy error estimate for the semidiscrete Galerkin method with an arbitrary choice of projection subspaces. Also, we establish some results on existence and uniqueness of an exact weak solution. We give an explicit error estimate for the finite element method and the Galerkin method in Mikhlin form.

Keywords

second-order hyperbolic equationthe Galerkin methoderror estimateweak solutionexistence and uniqueness of a solutionfinite element method

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • S. E. Zhelezovskii
    • 1
  1. 1.Saratov State Socio-Economic UniversitySaratov