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Error Estimates of the Galerkin Method for Quasilinear Hyperbolic Equations

Error Estimates of the Galerkin Method for Quasilinear Hyperbolic Equations Di erential Equations, Vol. 37, No. 7, 2001, pp. 988{997. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 7, 2001, pp. 941{949. Original Russian Text Copyright c 2001 by Zhelezovskii, Lyashko. NUMERICAL METHODS Error Estimates of the Galerkin Method for Quasilinear Hyperbolic Equations S. E. Zhelezovskii and A. D. Lyashko Povolzhsk Academy of Public Service, Kazan State University, Kazan, Russia Received March 1, 2001 INTRODUCTION We study the convergence of the semidiscrete Galerkin method for an abstract second-order quasilinear hyperbolic equation in a Hilbert space. We derive asymptotic error estimates in vari- ous norms without any restrictions on the nite-dimensional subspaces in which the approximate solutions must range. One of these estimates is order sharp in the corresponding class of exact solutions. The main results are stated in Theorems 1{4. The estimates given in Theorems 1 and 3 corre- spond to the natural smoothness of the exact solution of the original problem, and the estimates in Theorems 2 and 4 correspond to an increased smoothness of the exact solution. Here we primarily generalize the results of the paper [1] to the case in which the nonlinearity depends on the derivative of the unknown function and the derivative of the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Error Estimates of the Galerkin Method for Quasilinear Hyperbolic Equations

Zhelezovskii, S.; Lyashko, A.
Differential Equations , Volume 37 (7) – Oct 12, 2004
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References (5)

Publisher
Springer Journals
Copyright
Copyright © 2001 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1011965923024
Publisher site
See Article on Publisher Site

Abstract

Di erential Equations, Vol. 37, No. 7, 2001, pp. 988{997. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 7, 2001, pp. 941{949. Original Russian Text Copyright c 2001 by Zhelezovskii, Lyashko. NUMERICAL METHODS Error Estimates of the Galerkin Method for Quasilinear Hyperbolic Equations S. E. Zhelezovskii and A. D. Lyashko Povolzhsk Academy of Public Service, Kazan State University, Kazan, Russia Received March 1, 2001 INTRODUCTION We study the convergence of the semidiscrete Galerkin method for an abstract second-order quasilinear hyperbolic equation in a Hilbert space. We derive asymptotic error estimates in vari- ous norms without any restrictions on the nite-dimensional subspaces in which the approximate solutions must range. One of these estimates is order sharp in the corresponding class of exact solutions. The main results are stated in Theorems 1{4. The estimates given in Theorems 1 and 3 corre- spond to the natural smoothness of the exact solution of the original problem, and the estimates in Theorems 2 and 4 correspond to an increased smoothness of the exact solution. Here we primarily generalize the results of the paper [1] to the case in which the nonlinearity depends on the derivative of the unknown function and the derivative of the

Journal

Differential Equations – Springer Journals

Published: Oct 12, 2004

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