zbMATH — the first resource for mathematics

Bubble stabilization of finite element methods for the linearized incompressible Navier-Stokes equations. (English) Zbl 0887.76038
We discuss the stabilization, via bubble functions, of a finite element method for stationary linearized incompressible Navier-Stokes equations. It is shown that the upwind bubbles can be used to obtain the SUPG stabilization. Furthermore, the diffusion-dominated case is discussed in more detail, and it is also shown that in this regime the bubbles reproduce the right parameter of SUPG.

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: DOI
[1] Baiocchi, C.; Brezzi, F.; Franca, L.P., Virtual bubbles and gals, Comput. methods appl. mech. engrg., 105, 125-142, (1993)
[2] Brezzi, F.; Russo, A., Choosing bubbles for advection-diffusion problems, Math. models methods appl. sci., 4, 571-587, (1994) · Zbl 0819.65128
[3] Bank, R.E.; Welfert, B.D., A comparison between the mini-element and the Petrov-Galerkin formulations for the generalized Stokes problem, Comput. methods appl. mech. engrg., 83, 61-68, (1990) · Zbl 0732.65100
[4] Gresho, P.M., Some current CFD issues relevant to the incompressible Navier-Stokes equations, Comput. methods appl. mech. engrg., 87, 201-252, (1991) · Zbl 0760.76018
[5] Temam, R., Navier-Stokes equations, (1977), North-Holland Amsterdam · Zbl 0335.35077
[6] Ciarlet, P.G., The finite element method for elliptic problems, (1978), North-Holland Amsterdam · Zbl 0445.73043
[7] Brezzi, F., On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers, RAIRO ser. rouge, 8, 129-151, (1974) · Zbl 0338.90047
[8] Brezzi, F.; Fortan, M., Mixed and hybrid finite element methods, (1991), Springer-Verlag New York
[9] Johnson, C.; Nävert, U.; Pitkaranta, J., Finite element methods for linear hyperbolic problems, Comput. methods appl. mech. engrg., 45, 285-312, (1984) · Zbl 0526.76087
[10] Franca, L.P.; Frey, S.L., Stabilized finite element methods: II. the incompressible Navier-Stokes equations, Comput. methods appl. mech. engrg., 99, 209-233, (1992) · Zbl 0765.76048
[11] Franca, L.P.; Frey, S.L.; Hughes, T.J.R., Stabilized finite element methods: I. application to the advective-diffusive model, Comput. methods appl. mech. engrg., 95, 253-276, (1992) · Zbl 0759.76040
[12] Vishik, M.I.; Lyusternik, L.A.; Vishik, M.I.; Lyusternik, L.A., Regular degeneration and boundary layer for linear differential equations with a small parameter, Uspekki mat. nauk., Am. math. soc. transl. ser., 2, 20, 239-364, (1962) · Zbl 0122.32402
[13] A. Russo, A posteriori error estimators via bubble functions. Math. Models Methods Appl. Sci., in press. · Zbl 0853.65109
[14] Russo, A., A posteriori error estimators for the Stokes problem, Appl. math. lett., 8, 1-4, (1995) · Zbl 0821.65066
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.