AN ADAPTIVE WAVELET SOLUTION TO GENERALIZED STOKES PROBLEM

Abstract

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