An analysis for the compressible Stokes equations by first-order system of least-squares finite element method

This article applies the first-order system least-squares (fosls) finite element method developed by Cai, Manteuffel and McCormick to the compressible Stokes equations. By introducing a new dependent velocity flux variable, we recast the compressible Stokes equations as a first-order system. Then it is shown that the ellipticity and continuity hold for the least-squares functionals employing the mixture of H^-1 and L², so that the fosls finite element methods yield best approximations for the velocity flux and velocity.