Spectral Approximations of the Stokes Equations with Boundary Conditions on the Pressure

摘要

In this paper we study the approximation of the Stokes equation by spectral methods. The attention here is focused on the boundary conditions that are assigned to the pressure field on a part of the boundary. Several spectral discretizations are proposed and analyzed. The problem of the spurious modes related to these discretizations is, in particular, thoroughly investigated.