Abstract
The abstract problem discussed in Chapter I, § 4 lends itself readily to a straight-forward approximation that converges under reasonable assumptions with an error proportional to the approximation error of the spaces involved. When applied to the Stokes problem, this approach yields a conforming approximation of the velocity and pressure, although the approximate velocity field is (in general) not exactly divergence-free. The wide range of finite element methods developped in the remainder of the chapter are all founded on the material of this paragraph. Non-conforming methods can also be put into this framework (cf. Zine [85]) but for the sake of conciseness we have skipped them entirely.
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© 1986 Springer-Verlag Berlin Heidelberg
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Girault, V., Raviart, PA. (1986). Numerical Solution of the Stokes Problem in the Primitive Variables. In: Finite Element Methods for Navier-Stokes Equations. Springer Series in Computational Mathematics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61623-5_2
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DOI: https://doi.org/10.1007/978-3-642-61623-5_2
Publisher Name: Springer, Berlin, Heidelberg
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