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

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

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 GRIMAAG - Groupe de Recherche en Informatique et Mathématiques Appliquées Antilles-Guyane
4 Département de Mathématiques [Monastir]

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

Mots clés: Dynamical multi-level scheme; error analysis; Burgers equation; wavelet; hierarchical finite element method

Domaines: Analyse numérique [math.NA]

Arnaud Debussche, Jacques Laminie, Ezzeddine Zahrouni. A Dynamical Multi-level Scheme for the Burgers Equation: Wavelet and Hierarchical Finite Element. Journal of Scientific Computing, 2005, 25 (3), pp.445-497. ⟨10.1007/s10915-004-4806-4⟩. ⟨hal-00383423⟩