AN ADAPTIVE WAVELET SOLUTION TO GENERALIZED STOKES PROBLEM

Authors

1 Vali-e-Asr University of Rafsanjan Iran, Islamic Republic of

2 Shahid Bahonar University of Kerman Iran, Islamic Republic of

Abstract

In this paper we will present an adaptive wavelet scheme to solve
the generalized Stokes problem. Using divergence free wavelets, the
problem is transformed into an equivalent matrix vector system, that
leads to a positive definite system of reduced size for the
velocity. This system is solved iteratively, where the application
of the infinite stiffness matrix, that is sufficiently compressible,
is replaced by an adaptive approximation. Finally we prove that this
adaptive method has optimal computational complexity, that is it
recovers an approximate solution with desired accuracy at a
computational expense that stays proportional to the number of terms
in a corresponding wavelet-best N-term approximation.

Keywords