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A third-order boundary condition for the exterior Stokes problem in three dimensions

Author: Georges H. Guirguis
Journal: Math. Comp. 49 (1987), 379-389
MSC: Primary 65N30; Secondary 76-08, 76D07
MathSciNet review: 906177
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Abstract: We approximate the Stokes operator on an exterior domain in three dimensions by a truncated problem on a finite subdomain. A third-order artificial boundary condition is introduced. We discuss the approximating behavior of the truncated problem and its discretization in a finite element space. Combined errors arising from truncation and discretization are considered.

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  • [1] Robert A. Adams, Sobolev spaces, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and Applied Mathematics, Vol. 65. MR 0450957
  • [2] J. Boland, Finite Element and the Divergence Constraint for Viscous Flow, Ph.D. thesis, Carnegie-Mellon University, 1983.
  • [3] F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 8 (1974), no. R-2, 129–151 (English, with loose French summary). MR 0365287
  • [4] Murray Cantor, Numerical treatment of potential type equations on 𝑅ⁿ: theoretical considerations, SIAM J. Numer. Anal. 20 (1983), no. 1, 72–85. MR 687368, 10.1137/0720005
  • [5] Philippe G. Ciarlet, The finite element method for elliptic problems, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. Studies in Mathematics and its Applications, Vol. 4. MR 0520174
  • [6] 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 0343661
  • [7] V. Girault and P.-A. Raviart, Finite element approximation of the Navier-Stokes equations, Lecture Notes in Mathematics, vol. 749, Springer-Verlag, Berlin-New York, 1979. MR 548867
  • [8] C. I. Goldstein, The finite element method with nonuniform mesh sizes for unbounded domains, Math. Comp. 36 (1981), no. 154, 387–404. MR 606503, 10.1090/S0025-5718-1981-0606503-5
  • [9] Georges H. Guirguis, On the existence, uniqueness and regularity of the exterior Stokes problem in 𝑅³, Comm. Partial Differential Equations 11 (1986), no. 6, 567–594. MR 837276, 10.1080/03605308608820437
  • [10] Georges H. Guirguis and Max D. Gunzburger, On the approximation of the exterior Stokes problem in three dimensions, RAIRO Modél. Math. Anal. Numér. 21 (1987), no. 3, 445–464 (English, with French summary). MR 908240
  • [11] G. H. Guirguis, On the Existence, Uniqueness, Regularity and Approximation of the Exterior Stokes Problem in $ {R^3}$, Ph.D. Thesis, University of Tennessee, Knoxville, 1983.
  • [12] Alvin Bayliss, Max Gunzburger, and Eli Turkel, Boundary conditions for the numerical solution of elliptic equations in exterior regions, SIAM J. Appl. Math. 42 (1982), no. 2, 430–451. MR 650234, 10.1137/0142032
  • [13] B. Hanouzet, Espaces de Sobolev avec poids application au problème de Dirichlet dans un demi espace, Rend. Sem. Mat. Univ. Padova 46 (1971), 227–272 (French). MR 0310417
  • [14] O. A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Second English edition, revised and enlarged. Translated from the Russian by Richard A. Silverman and John Chu. Mathematics and its Applications, Vol. 2, Gordon and Breach, Science Publishers, New York-London-Paris, 1969. MR 0254401
  • [15] J. L. Lions & E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Springer-Verlag, New York, 1972.

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Article copyright: © Copyright 1987 American Mathematical Society