An explicit finite element method for convection- dominated compressible viscous Stokes system with inflow boundary

Abstract

A linearized steady-state compressible viscous Stokes system with inflow boundary is considered on a plane domain. An explicit finite element method for the system is presented with convection-dominance and 0(h) viscous numbers where h is a given mesh size. With small viscous numbers it is a degenerate hyperbolic problem and also the Dirichlet boundary condition may generate a layer near the outflow boundary. The method is applied over a triangulation of the domain in an explicit fashion from triangle to triangle and gives a continuous nth degree piecewise polynomial approximation. We show a local stability and a global one for the method and derive error estimates for each variable of velocity, pressure and their derivatives. It is observed that the compressibility number K := rho'/rho is an essential ingredient in showing our stability results. (C) 2003 Elsevier B.V. All rights reserved.