An analysis of the finite element method using Lagrange multipliers for the stationary Stokes equations

Falk, Richard S.

doi:10.1090/S0025-5718-1976-0403260-0

An analysis of the finite element method using Lagrange multipliers for the stationary Stokes equations

Author: Richard S. Falk
Journal: Math. Comp. 30 (1976), 241-249
MSC: Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-1976-0403260-0
MathSciNet review: 0403260
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Abstract: An error analysis is presented for the approximation of the stationary Stokes equations by a finite element method using Lagrange multipliers.

Approximation by hill functions, Comment. Math. Univ. Carolinae 11 (1970), 787–811. MR 292309

I. BABUŠKA, Approximation by Hill Functions. II, Technical Note BN-708, Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, 1971.

Ivo Babuška, The finite element method with Lagrangian multipliers, Numer. Math. 20 (1972/73), 179–192. MR 359352, DOI https://doi.org/10.1007/BF01436561
A. K. Aziz (ed.), The mathematical foundations of the finite element method with applications to partial differential equations, Academic Press, New York-London, 1972. MR 0347104
M. Crouzeix and P.-A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 7 (1973), no. R-3, 33–75. MR 343661

R. S. FALK, "An analysis of the penalty method and extrapolation for the stationary Stokes equations," in Advances in Computer Methods for Partial Differential Equations, R. Vichnevetsky (editor), Proceedings of the AICA Symposium, Lehigh Univ., June, 1975, pp. 66-69.

Richard S. Falk and J. Thomas King, A penalty and extrapolation method for the stationary Stokes equations, SIAM J. Numer. Anal. 13 (1976), no. 5, 814–829. MR 471382, DOI https://doi.org/10.1137/0713064
Richard S. Falk, A finite element method for the stationary Stokes equations using trial functions which do not have to satisfy ${\rm div}\nu =0$, Math. Comp. 30 (1976), no. 136, 698–702. MR 421109, DOI https://doi.org/10.1090/S0025-5718-1976-0421109-7
Richard S. Falk, A Ritz method based on a complementary variational principle, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. 10 (1976), no. R-2, 39–48 (English, with Loose French summary). MR 0433915

R. B. KELLOGG & J. E. OSBORN, A Regularity Result for the Stokes Problem in a Convex Polygon, Technical Note BN-804, Institute for Fluid Dynamics and Applied Mathematics University of Maryland, 1974.

O. A. LADYŽENSKAJA, The Mathematical Theory of Viscous Incompressible Flow, Fizmatigiz, Moscow, 1961; English transl., Gordon and Breach, New York, 1962. MR 27 #5034a, b.

J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 1, Travaux et Recherches Mathématiques, No. 17, Dunod, Paris, 1968 (French). MR 0247243

R. TEMAM, On the Theory and Numerical Analysis of the Navier-Stokes Equations, Lecture Note #9, University of Maryland, June, 1973.