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

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 O(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 κ≔ρ′/ρ is an essential ingredient in showing our stability results.