Conservation of mass and momentum of the least-squares spectral collocation scheme for the Stokes problem

From the literature it is known that spectral least-squares schemes perform poorly with respect to mass conservation and compensate this lack by a superior conservation of momentum. This should be revised, since the here presented new least-squares spectral collocation scheme leads to an outstanding performance with respect to conservation of momentum and mass. The reasons can be found in using only a few elements, each with high polynomial degree, avoiding normal equations for solving the overdetermined linear systems of equations and by introducing the Clenshaw–Curtis quadrature rule for imposing the average pressure to be zero. Furthermore, we combined the transformation of Gordon and Hall (transfinite mapping) with our least-squares spectral collocation scheme to discretize the internal flow problems.