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hal-00383423, version 1

A Dynamical Multi-level Scheme for the Burgers Equation: Wavelet and Hierarchical Finite Element

Arnaud Debussche () 1, Jacques Laminie () 2, 3, Ezzeddine Zahrouni 4

Journal of Scientific Computing 25, 3 (2005) 445-497

Abstract: Algorithms issued from the NonLinear Galerkin method have been used in many situations and with different discretizations for the resolution of evolutionary nonlinear equations. The main idea of these methods is to use a splitting of the solution in order to model the equation. According to the splitting of the solution, a splitting of the equation is obtained. The modeling principle is to freeze terms which have a small time variation. In this work we use wavelet discretizations of the 2-D Burgers equations and compare the results with the hierarchical finite elements method. The numerical tests indicate that wavelets give better results than finite elements

  • 1:  Institut de Recherche Mathématique de Rennes (IRMAR)
  • CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne
  • 2:  Laboratoire de Mathématiques d'Orsay (LM-Orsay)
  • CNRS : UMR8628 – Université Paris XI - Paris Sud
  • 3:  Groupe de Recherche en Informatique et Mathématiques Appliquées Antilles-Guyane (GRIMAAG)
  • Université des Antilles et de la Guyane
  • 4:  Département de Mathématiques [Monastir]
  • Faculté des Sciences de Monastir
  • Domain : Mathematics/Numerical Analysis
  • Keywords : Dynamical multi-level scheme – error analysis – Burgers equation – wavelet – hierarchical finite element method
 
  • hal-00383423, version 1
  • http://hal.archives-ouvertes.fr/hal-00383423
  • oai:hal.archives-ouvertes.fr:hal-00383423
  • From: Dominique Hervé <>
  • Submitted on: Wednesday, 13 May 2009 09:25:22
  • Updated on: Thursday, 18 March 2010 15:48:37