A posteriori error estimates for the Stokes equations: A comparison. (English) Zbl 0725.65106

The authors consider three estimates based on resolution of a local Stokes problem and one based on residuals, giving some theoretical comparison inequalities and examining their numerical behaviour on test problems.


65Z05 Applications to the sciences
65N15 Error bounds for boundary value problems involving PDEs
35Q30 Navier-Stokes equations
Full Text: DOI


[1] Babuška, I.; Zienkiewicz, O.C.; Gago, J.; de A. Oliveira, E.R., Accuracy estimates and adaptive refinements in finite element computations, (1986), Wiley New York · Zbl 0663.65001
[2] Glowinski, R.; Periaux, J.F., Numerical methods for nonlinear problems in fluid dynamics, () · Zbl 0595.76059
[3] Babuška, I.; Rheinboldt, W.C., A posteriori error estimates for the finite element method, Internat. J. numer. methods engrg., 12, 1597-1615, (1978) · Zbl 0396.65068
[4] Abdalass, E.M., Resolution performante du probleme de Stokes par mini-elements, maillage auto-adaptatifs et methodes multigrilles-applications, ()
[5] Bank, R.E., Analysis of a local a posteriori error estimate for elliptic equations, (), 119-128
[6] Bank, R.E.; Weiser, A., Some a posteriori error estimators for partial differential equations, Math. comp., 44, 283-301, (April 1985)
[7] Verfürth, R., A posteriori error estimators for the Stokes equations, Numer. math., 55, 309-325, (1989) · Zbl 0674.65092
[8] R.E. Bank and B.D. Welfert, A posteriori error estimates for the Stokes problem (to appear). · Zbl 0731.76040
[9] Bank, R.E.; Welfert, B.D.; Yserentant, H., A class of iterative methods for solving saddle point problems, Numer. math., 56, 645-666, (1990) · Zbl 0684.65031
[10] Arnold, D.N.; Brezzi, F.; Fortin, M., A stable finite element for the Stokes equations, Calcolo, 21, 337-344, (1984) · Zbl 0593.76039
[11] Brezzi, F.; Douglas, J., Stabilized mixed methods for the Stokes problem, Numer. math., 53, 225-235, (1988) · Zbl 0669.76052
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.