Adaptive biorthogonal spline schemes for advection–reaction equations

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.