On the limitations of bubble functions. (English) Zbl 0847.76033

Summary: We present two examples that demonstrate no advantage in enriching a finite element subspace with bubble functions.


76M10 Finite element methods applied to problems in fluid mechanics
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[1] Farhat, C.; Sobh, N., A coarse/fine preconditioner for very ill-conditioned finite element problems, Internat. J. numer. methods engrg., 28, 1715-1723, (1989) · Zbl 0724.73213
[2] Ciarlet, P.G., Basic error estimates for elliptic problems, (), (Part 1) · Zbl 0875.65086
[3] Farhat, C., On the h refinement of triangular meshes, ()
[4] Baiocchi, C.; Brezzi, F.; Franca, L.P., Virtual bubbles and the Galerkin-least-squares method, Comput. methods appl. mech. engrg., 105, 125-141, (1993) · Zbl 0772.76033
[5] Brezzi, F.; Bristeau, M.O.; Franca, L.P.; Mallet, M.; Rogé, G., A relationship between stabilized finite element methods and the Galerkin method with bubble functions, Comput. methods appl. mech. engrg., 96, 117-129, (1992) · Zbl 0756.76044
[6] Brooks, A.N.; Hughes, T.J.R., Streamline upwind/Petrov-Galerkin formulations for convective dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. methods appl. mech. engrg., 32, 199-259, (1982) · Zbl 0497.76041
[7] Arnold, D.N.; Brezzi, F.; Fortin, M., A stable finite element for the Stokes equations, Calcolo, 23, 337-344, (1984) · Zbl 0593.76039
[8] Hughes, T.J.R.; Franca, L.P.; Balestra, M., A new finite element formulation for computational fluid dynamics: V. circumventing the babuška-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations, Comput. methods in appl. mech. engrg., 59, 85-99, (1986) · Zbl 0622.76077
[9] Pierre, R., Simple C0 approximations for the computation of incompressible flows, Comput. methods appl. mech. engrg., 68, 205-227, (1988) · Zbl 0628.76040
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