Journal of the
Korean Mathematical Society JKMS

We formulate and study a finite element method for a linearized steady state, compressible, viscous Navier-Stokes equations in 2D, based on the discontinuous Galerkin method. Dislike the standard discontinuous Galerkin method, we do not assume that the triangle sides be bounded away from the characteristic direction. The unique stability follows from the inf-sup condition established on the finite dimensional spaces for the (incompressible) Stokes problem. An error analysis having a jump discontinuity for pressure is shown.

Keywords: compressible viscous Stokes flows, continuity equation, finite element method

MSC numbers: 65N15, 35M10