Ten lectures on wavelets
Journal of Computational Physics
Adaptive wavelet methods for elliptic operator equations: convergence rates
Mathematics of Computation
Development of CFL-Free, Explicit Schemes for Multidimensional Advection-Reaction Equations
SIAM Journal on Scientific Computing
Adaptive Wavelet Schemes for Elliptic Problems---Implementation and Numerical Experiments
SIAM Journal on Scientific Computing
Fully adaptive multiresolution finite volume schemes for conservation laws
Mathematics of Computation
Hi-index | 31.45 |
In this paper, based on Eulerian-Lagrangian localized adjoint method (ELLAM), we use biorthogonal spline wavelets to develop numerical schemes for multidimensional advection-reaction equations. The derived schemes produce accurate numerical solutions even if large time steps are used. These schemes are explicit but unconditionally stable. They also have the ability to carry out adaptive compression while preserving the total mass. Numerical experiments including observations on their convergence rates are presented to show the strong potential of these methods.