An analysis of the finite element method using Lagrange multipliers for the stationary Stokes equations
Author:
Richard S. Falk
Journal:
Math. Comp. 30 (1976), 241249
MSC:
Primary 65N30
MathSciNet review:
0403260
Fulltext PDF Free Access
Abstract 
References 
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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.
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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. 6669.
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Richard
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Stokes equations, SIAM J. Numer. Anal. 13 (1976),
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Richard
S. Falk, A finite element method for the
stationary Stokes equations using trial functions which do not have to
satisfy 𝑑𝑖𝑣𝜈=0, Math. Comp. 30 (1976), no. 136, 698–702. MR 0421109
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Richard
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Opérationnelle Sér. \jname RAIRO Analyse Numérique
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R. B. KELLOGG & J. E. OSBORN, A Regularity Result for the Stokes Problem in a Convex Polygon, Technical Note BN804, Institute for Fluid Dynamics and Applied Mathematics University of Maryland, 1974.
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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.
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Magenes, Problèmes aux limites non homogènes et
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R. TEMAM, On the Theory and Numerical Analysis of the NavierStokes Equations, Lecture Note #9, University of Maryland, June, 1973.
 [1]
 I. BABUŠKA, "Approximation by Hill functions," Comment. Math. Univ. Carolinae, v. 11, 1970, pp. 787811. MR 45 #1396. MR 0292309 (45:1396)
 [2]
 I. BABUŠKA, Approximation by Hill Functions. II, Technical Note BN708, Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, 1971.
 [3]
 I. BABUŠKA, "The finite element method with Lagrangian multipliers," Numer. Math. v. 20, 1973, pp. 179192. MR 0359352 (50:11806)
 [4]
 I. BABUŠKA, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equtions, A. K. Aziz (editor), Academic Press, New York, 1972. MR 0347104 (49:11824)
 [5]
 M. CROUSEIX & P. RAVIART, Conforming and Nonconforming Finite Element Methods for Solving the Stationary Stokes Equations. I, Revue Française d'Automatique, Informatique et Recherche Operationelle, 7 année, decembre 1973, R3, pp. 3376. MR 0343661 (49:8401)
 [6]
 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. 6669.
 [7]
 R. S. FALK & J. T. KING, "A penalty and extrapolation method for the stationary Stokes equations," SIAM J. Numer. Anal. (To appear.) MR 0471382 (57:11116)
 [8]
 R. S. FALK, "A finite element method for the stationary Stokes equations using trial functions which do not have to satisfy ," Math. Comp. (To appear.) MR 0421109 (54:9114)
 [9]
 R. S. FALK, A Ritz Method Based on a Complimentary Variational Principle, Revue Francaise d'Automatique, Informatique et Recherche Operationelle. (To appear.) MR 0433915 (55:6885)
 [10]
 R. B. KELLOGG & J. E. OSBORN, A Regularity Result for the Stokes Problem in a Convex Polygon, Technical Note BN804, Institute for Fluid Dynamics and Applied Mathematics University of Maryland, 1974.
 [11]
 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.
 [12]
 J.L. LIONS & E. MAGENES, Problèmes aux limites non homogènes et applications, Vol. 1, Travaux et Recherches Mathématiques, no. 17, Dunod, Paris, 1968. MR 40 #512. MR 0247243 (40:512)
 [13]
 R. TEMAM, On the Theory and Numerical Analysis of the NavierStokes Equations, Lecture Note #9, University of Maryland, June, 1973.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197604032600
PII:
S 00255718(1976)04032600
Article copyright:
© Copyright 1976
American Mathematical Society
