AN ADAPTIVE WAVELET SOLUTION TO GENERALIZED STOKES PROBLEM
الموضوعات : فصلنامه ریاضیHassan Jamali 1 , Ataollah Askari Hemmat 2
1 - Vali-e-Asr University of Rafsanjan
Iran, Islamic Republic of
2 - Shahid Bahonar University of Kerman
Iran, Islamic Republic of
الکلمات المفتاحية: Wavelet basis, Riesz basis, Adaptive solution, N-term approximation, Galerkin approximation,
ملخص المقالة :
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.
