Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

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
DOI: https://doi.org/10.1090/S0025-5718-1987-0906177-5
MathSciNet review: 906177
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975. MR 0450957 (56:9247)
  • [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," RAIRO Anal. Numér. Sér. Rouge, v. 8, 1974, pp. 129-151. MR 0365287 (51:1540)
  • [4] M. Cantor, "Numerical treatment of potential type equations on $ {R^n}$: Theoretical considerations," SIAM J. Numer. Anal., v. 20, 1983, pp. 72-85. MR 687368 (84g:65144)
  • [5] P. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. MR 0520174 (58:25001)
  • [6] M. Crouzeix & P. Raviart, "Conforming and non-conforming finite element methods for solving the stationary Stokes equation," RAIRO Anal. Numér. Sér. Rouge, v. 7, 1973, pp. 33-75. MR 0343661 (49:8401)
  • [7] V. Girault & P. Raviart, Finite Element Approximation of the Navier-Stokes Equations, Lecture Notes in Math., vol. 749, Springer-Verlag, Berlin and New York, 1979. MR 548867 (83b:65122)
  • [8] C. Goldstein, "The finite element method with non-uniform mesh sizes for unbounded domains," Math. Comp., v. 36, 1981, pp. 387-404. MR 606503 (82b:65121)
  • [9] G. H. Guirguis, "On the existence, uniqueness and regularity of the exterior Stokes problem in $ {R^3}$," Comm. Partial Differential Equations, v. 11, 1986, pp. 567-594. MR 837276 (87j:35296)
  • [10] G. H. Guirguis & M. D. Gunzburger, "On the approximation of the exterior Stokes problem in three dimensions," RAIRO Anal. Numér. (To appear.) MR 908240 (88m:76028)
  • [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 & Eli Turkel, "Boundary conditions for the numerical solution of elliptic equations in exterior regions," SIAM J. Appl. Math., v. 42, 1982, pp. 430-451. MR 650234 (84h:65108)
  • [13] B. Hanouzet, "Espaces de Sobolev avec poids. Application a un problème de Dirichlet dans un demi-espace," Rend. Sem. Mat. Univ. Padova, v. 46, 1971, pp. 227-272. MR 0310417 (46:9517)
  • [14] O. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York, 1969. MR 0254401 (40:7610)
  • [15] J. L. Lions & E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Springer-Verlag, New York, 1972.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N30, 76-08, 76D07

Retrieve articles in all journals with MSC: 65N30, 76-08, 76D07


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1987-0906177-5
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society