Abstract
This paper deals with the spectral element discretization of the Navier-Stokes equations in a disk with discontinuous boundary data, which is known as the driven cavity problem. The numerical treatment does not involve any regularization of these data. Relying on a variational formulation in the primitive variables of velocity and pressure, we describe a discretization of these equations and derive error estimates in appropriate weighted Sobolev spaces. We propose an algorithm to solve the nonlinear discrete system and present numerical experiments to verify its efficiency.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Belhachmi, Z., Bernardi, C. & Karageorghis, A. Spectral Element Discretization of the Circular Driven Cavity. Part IV: The Navier-Stokes Equations. J. math. fluid mech. 6, 121–156 (2004). https://doi.org/10.1007/s00021-003-0101-7
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s00021-003-0101-7