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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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An analysis of the finite element method using Lagrange multipliers for the stationary Stokes equations
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by Richard S. Falk PDF
Math. Comp. 30 (1976), 241-249 Request permission

Abstract:

An error analysis is presented for the approximation of the stationary Stokes equations by a finite element method using Lagrange multipliers.
References
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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. 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 10.1137/0713064
  • Richard S. Falk, A finite element method for the stationary Stokes equations using trial functions which do not have to satisfy $\textrm {div}\nu =0$, Math. Comp. 30 (1976), no. 136, 698–702. MR 421109, DOI 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.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Math. Comp. 30 (1976), 241-249
  • MSC: Primary 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-1976-0403260-0
  • MathSciNet review: 0403260