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A stable finite element for the Stokes equations. (English) Zbl 0593.76039
Summary: We present in this paper a new velocity-pressure finite element for the computation of Stokes flow. We discretize the velocity field with continuous piecewise linear functions enriched by bubble functions, and the pressure by piecewise linear functions. We show that this element satisfies the usual inf-sup condition and converges with first order for both velocities and pressure. Finally we relate this element to families of higher order elements and to the popular Taylor-Hood element.

MSC:
76D07 Stokes and related (Oseen, etc.) flows
35Q30 Navier-Stokes equations
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