Galerkin modelling of the Burgers equation using harmonic wavelets. (English) Zbl 1044.65511

Summary: In this paper we present a wavelet Galerkin approximation of the one-dimensional Burgers equation using complex harmonic wavelets. We derive exact expressions for the connection coefficients for the linear dissipation and nonlinear advection terms. A large reduction in the number of space-scale nonlinear modes is obtained by exploiting the band-limited spectra and localisation properties of harmonic wavelets. We discuss the advantages and disadvantages of implementing harmonic wavelets as opposed to the more standard choice of wavelets basis, highlighting the relevance to shell models of turbulence.


65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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