Analysis and Computation of Least-squares Methods for a Compressible Stokes Problem

We develop and analyze a negative norm least-squares method for the compressible Stokes equations with an inflow boundary condition. Least-squares principles are derived for a first-order form of the equations obtained by using ω = ∇ × u and φ = ∇ ·u as new dependent variables. The resulting problem is incompletely elliptic, i.e., it combines features of elliptic and hyperbolic equations. As a result, wellposedness of least-squares functionals cannot be established using the ADN elliptic theory and so we use direct approaches to prove their norm-equivalence. The article concludes with numerical examples that illustrate the theoretical convergence rates. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 22: 000–000, 2006