A mixed problem and its approximation in an abstract framework are considered. They are proved to be well posed if and only if several inf-sup conditions are satisfied. These results are applied to the Stokes equations in a square, formulated in Chebyshev weighted Sobolev spaces and their approximations. Two kinds of spectral discretizations are analyzed: a Galerkin method and a collocation method at the Chebyshev nodes.
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Bernardi et al. (1988) studied this question.
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