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.

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