A wavelet-based adaptive finite element method for advection-diffusion equations

We propose a wavelet-based procedure for adapting a finite element mesh to the structure of the solution. After a finite element solution is computed on a given unstructured mesh, it is wavelet-analyzed on a superimposed regular dyadic grid; the analysis leads to an adapted distribution of grid points, which defines the new unstructured mesh via a Delaunay triangulation. Several examples of discretizations of steady convection-diffusion problems in the convection-dominated regime indicate the feasibility of our approach.