Using divergence free wavelets for the numericalsolution of the
نویسنده
چکیده
The divergence free formulation of the Stokes problem leads to a positive deenite system of reduced size for the velocity, provided that divergence free trial spaces are available. The pressure is eliminated and can eeciently be computed by a post-processing procedure. In this paper we use divergence free wavelets to construct corresponding trial spaces for a Galerkin scheme. We describe the construction, prove error estimates for the resulting scheme and show some numerical results.
منابع مشابه
Numerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets
In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets to solve the integral equation. Numerical implementation of the method is illustrated by two ben...
متن کاملAN ADAPTIVE WAVELET SOLUTION TO GENERALIZED STOKES PROBLEM
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 r...
متن کاملDivergence-Free Multiwavelets
In this paper we construct IR n-valued biorthogonal, compactly supported multiwavelet families such that one of the biorthogo-nal pairs consists of divergence-free vector wavelets. The construction is based largely on Lemari e's idea of multiresolution analyses intertwined by diierentiation. We show that this technique extends nontrivially to multiwavelets via Strela's two-scale transform. An e...
متن کاملDirect Numerical Simulation of Turbulence Using Divergence-Free Wavelets
We present a numerical method based on divergence-free wavelets to solve the incompressible Navier-Stokes equations. We introduce a new scheme which uses anisotropic (or generalized) divergence-free wavelets, and which only needs Fast Wavelet Transform algorithms. We prove its stability and show convincing numerical experiments.
متن کاملFault Strike Detection Using Satellite Gravity Data Decomposition by Discrete Wavelets: A Case Study from Iran
Estimating the gravity anomaly causative bodies boundary can facilitate the gravity field interpretation. In this paper, 2D discrete wavelet transform (DWT) is employed as a method to delineate the boundary of the gravity anomaly sources. Hence, the GRACE’ satellite gravity data is decomposed using DWT. DWT decomposites a single approximation coefficients into four distinct components: the appr...
متن کامل