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

Authors:
A. Debussche;J. Laminie;E. Zahrouni
Affiliations:
E.N.S. Cachan, Antenne de Bretagne, Rennes, France;Laboratoire de Mathématique, Université de Paris-Sud, Orsay, France;Département de Mathématiques, Faculté des Sciences de Monastir, E. Zahrouni, Tunisie
Venue:
Journal of Scientific Computing
Year:
2005

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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