On mass conservation in least-squares methods
We compare three least-squares finite element reformulations of the Stokes equations, paying particular attention to mass conservation. The first problem we approximate has a simple analytical solution over a convex region. Even for this simple problem, without special treatment of the conservation of mass term, very poor numerical solutions may result. Sufficiently weighting this term leads to a dramatic improvement in the results over a range of test problems.
least-squares finite elements conservation of mass first-order stokes flows stress and stream functions