AN ADAPTIVE WAVELET SOLUTION TO GENERALIZED STOKES PROBLEM

Subject Areas : International Journal of Mathematical Modelling & Computations

Hassan Jamali ¹ ( Vali-e-Asr University of Rafsanjan Iran, Islamic Republic of )
Ataollah Askari Hemmat ² ( Shahid Bahonar University of Kerman Iran, Islamic Republic of )

Received: 2016-04-15 Accepted : 2016-04-15 Published : 2014-03-21

Keywords: Wavelet basis, Riesz basis, Adaptive solution, N-term approximation, Galerkin approximation,

Abstract :

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