A Galerkin finite element approach to Burgers' equation

DOĞAN A.

APPLIED MATHEMATICS AND COMPUTATION, vol.157, no.2, pp.331-346, 2004 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 157 Issue: 2
  • Publication Date: 2004
  • Doi Number: 10.1016/j.amc.2003.08.037
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.331-346
  • Keywords: Burgers' equation, finite element methods, Galerkin, NUMERICAL-SOLUTION
  • Abdullah Gül University Affiliated: Yes

Abstract

A Galerkin finite element method is presented for the numerical solution of Burgers' equation. A linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is found via a Crank-Nicolson approach involving a product approximation. It is shown that this method is capable of solving Burgers' equation accurately for a wide range of viscosity values. The results show that the new method performs better than the most of the methods available in the literature. (C) 2003 Elsevier Inc. All rights reserved.