A direct solver for the least-squares spectral collocation system on rectangular elements for the Stokes equations
نویسندگان
چکیده
A least-squares spectral collocation scheme for the steady and unsteady Stokes equations is proposed. The original domain is decomposed into quadrilateral subelements and on the element interfaces continuity of the functions is enforced in the least-squares sense. The collocation conditions and the interface conditions lead to overdetermined systems. These systems are directly solved by QR decomposition of the underlying matrices. By numerical simulations it is shown that the direct method leads to better results than the approach with normal equations. Furthermore it is shown that the condition numbers can be reduced by introducing the Clenshaw-Curtis quadrature rule for imposing the average pressure to be zero.
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