In this paper we introduce an adaptive collocation scheme for the solution of time independent partial differential equations. Such a technique is based on the interpolating multiresolution analysis. The method defines a sequence of grids, each one computed by looking at the interpolating wavelet transform of the solution of the problem on the previous grid. The computational cost of the solution of each problem is kept low by either applying a Schur complement technique or by coupling the refining procedure with an iterative solver. The method is tested on some two dimensional test problems, both of linear and non linear type.
"Adaptive wavelet collocation for the solution of steady-state equations", Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); doi: 10.1117/12.205453; https://doi.org/10.1117/12.205453