×

Analysis of a mixed finite element for the Stokes problem. I: General results. (Analyse d’un élément mixte pour le problème de Stokes. I: Résultats généraux.) (French. English summary) Zbl 0765.65113

The authors presents some variants of standard a priori error estimates for mixed finite element methods. In particular, these variants including dual estimates in the spirit of Aubin-Nitsche apply to a situation with more than two variables where the coerciveness assumption is much weaker than in the classical case and where the “inclusion of kernels property” is only partially satisfied.

MSC:

65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
76D07 Stokes and related (Oseen, etc.) flows
35Q30 Navier-Stokes equations

Citations:

Zbl 0765.65114
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Aubin, J.P. (1972): Approximation of elliptic boundary-value problems. Wiley, New York · Zbl 0248.65063
[2] Babuska, I. (1972): The finite element method with Lagrange multipliers. Numer. Math.20, 179-192 · Zbl 0258.65108 · doi:10.1007/BF01436561
[3] Brezzi, F. (1974): On the Existence, Uniqueness and Approximation of Saddle-Point Problems Arising from Lagrangian Multipliers. R.A.I.R.O.8, R2, 129-151 · Zbl 0338.90047
[4] Brezzi, F., Fortin M. (1991): Mixed and Hybrid Finite Element Methods. Springer, Berlin Heidelberg New York · Zbl 0788.73002
[5] Brezzi, F., Raviart, P.A. (1976): Mixed Finite Element Methods for 4th Order Elliptic Equations. Proc. Royal Irish Academy Conference on Numerical Analysis · Zbl 0434.65085
[6] Falk, R.S., Osborn, J.E. (1980): Error Estimates for Mixed Methods. R.A.I.R.O. Anal. Num?r.14, No. 3, 269-277 · Zbl 0467.65062
[7] Fortin, M. (1977): An Analysis of the Convergence of Mixed Finite Element Methods. R.A.I.R.O. Anal. Numer.11, 341-354 · Zbl 0373.65055
[8] Fortin, M., Mghazli, Z. (1992): Analyse d’un ?l?ment mixte pour le probl?me de Stokes. II. Construction et estimations d’erreur. Numer. Math.61, 161-188 · Zbl 0765.65114 · doi:10.1007/BF01396225
[9] Douglas, J., Roberts, J.E. (1985): Global estimates for mixed methods for second order elliptic equations. Math. Comput.44, 39-52 · Zbl 0624.65109 · doi:10.1090/S0025-5718-1985-0771029-9
[10] Girault, V., Raviart, P.A. (1979): Finite Element Approximation of Navier-Stokes Equations. Lectures Notes in Math. 749. Springer, Berlin, Heidelberg New York · Zbl 0413.65081
[11] Nitsche, J. (1968): Ein Kriterium f?r die Quasi-Optimalitat des Ritzschen Verfahrens. Numer. Math.11, 346-348 · Zbl 0175.45801 · doi:10.1007/BF02166687
[12] Roberts, J.E., Thomas, J.M. (1990): Mixed and hybrid methods. Handbook of Numerical Analysis, Vol. II. Finite Element Methods. North Holland, Amsterdam
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.