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Li, Jian; He, Yinnian

A stabilized finite element method based on two local Gauss integrations for the Stokes equations. (English) Zbl 1132.35436

J. Comput. Appl. Math. 214, No. 1, 58-65 (2008).
Summary: This paper considers a stabilized method based on the difference between a consistent and an under-integrated mass matrix of the pressure for the Stokes equations approximated by the lowest equal-order finite element pairs. This method offsets only the discrete pressure space by subtracting the simple and symmetrical term at element level in order to circumvent the inf-sup condition. Optimal error estimates are obtained by applying the standard Galerkin technique. Finally, the numerical illustrations are presented completely in agree with the theoretical expectations.

Cited in 1 Review
Cited in 144 Documents

MSC:

35Q30 Navier-Stokes equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76M10 Finite element methods applied to problems in fluid mechanics

Keywords:

Stokes equations; penalty method; stable Galerkin method; inf-sup condition
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\textit{J. Li} and \textit{Y. He}, J. Comput. Appl. Math. 214, No. 1, 58--65 (2008; Zbl 1132.35436)
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References:

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