199	1997	Mats Holmström	matsh@tdb.uu.se	An Adaptive Finite Difference Method for Time Dependent PDEs

                            Abstract

A method is presented for adaptively solving time dependent PDEs. The
method is based on an interpolating wavelet transform using polynomial
interpolation on dyadic grids.  The adaptability is performed by
choosing the representation based on the magnitude of the wavelet
coefficients.  Any finite difference discretization can then be used.
As a numerical example the time dependent, compressible, Navier-Stokes
equations are solved for flow over a flat plate using centered finite
differences.  It is found that the proposed method outperforms a
finite difference method on a uniform grid in terms of CPU time when a
highly accurate solution is wanted.