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Bank, Randolph E.; Welfert, Bruno D.

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

Comput. Methods Appl. Mech. Eng. 82, No. 1-3, 323-340 (1990).
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.
Reviewer: J.D.P.Donnelly (Oxford)

Cited in 30 Documents

MSC:

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

Keywords:

a posteriori error estimates; Stokes equations; finite elements; comparison; test problems
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\textit{R. E. Bank} and \textit{B. D. Welfert}, Comput. Methods Appl. Mech. Eng. 82, No. 1--3, 323--340 (1990; Zbl 0725.65106)
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References:

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[2] Glowinski, R.; Periaux, J.F., Numerical methods for nonlinear problems in fluid dynamics, () · Zbl 0595.76059
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[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
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