Wavelet based schemes for linear advection–dispersion equation

In this paper, two wavelet based adaptive solvers are developed for linear advection–dispersion equation. The localization properties and multilevel structure of the wavelets in the physical space are used for adaptive computational methods for solution of equation which exhibit both smooth and shock-like behaviour. The first framework is based on wavelet-Galerkin and the second is based on multiscale decomposition of finite element method. Coiflet wavelet filter is incorporated in both the methods. The main advantage of both the adaptive methods is the elimination of spurious oscillations at very high Peclet number.