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

  • Authors:

  • Jae Ryong Kweon;Philsu Kim

  • Affiliations:

  • Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, South Korea;Major in Mathematics, Dong-A University, 840, Hadan-2 Dong, Saha-Ku, Pusan 604-714, South Korea

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2003

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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 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.