On variational formulations for the Stokes equations with nonstandard boundary conditions

James H. Bramble; Ping Lee

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1994)

  • Volume: 28, Issue: 7, page 903-919
  • ISSN: 0764-583X

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Bramble, James H., and Lee, Ping. "On variational formulations for the Stokes equations with nonstandard boundary conditions." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 28.7 (1994): 903-919. <http://eudml.org/doc/193764>.

@article{Bramble1994,
author = {Bramble, James H., Lee, Ping},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {weak formulations; no divergence constraints; error estimates},
language = {eng},
number = {7},
pages = {903-919},
publisher = {Dunod},
title = {On variational formulations for the Stokes equations with nonstandard boundary conditions},
url = {http://eudml.org/doc/193764},
volume = {28},
year = {1994},
}

TY - JOUR
AU - Bramble, James H.
AU - Lee, Ping
TI - On variational formulations for the Stokes equations with nonstandard boundary conditions
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1994
PB - Dunod
VL - 28
IS - 7
SP - 903
EP - 919
LA - eng
KW - weak formulations; no divergence constraints; error estimates
UR - http://eudml.org/doc/193764
ER -

References

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  1. [1] S. AGMON, A. DOUGLIS, L. NIRENBERG, 1964, Estimates Near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions II, Comm. Pure Appl. Math., 17, 35-92. Zbl0123.28706MR162050
  2. [2] C. BEGUE, C. CONCA, F. MURAT, O. PIRONNEAU, 1989, Les équations de Stokes et de Navier-Stokes avec des conditions aux limites sur la pression, Nonlinear Partial Differential Equations and Their Applications, College de France Seminar, Pitman Res. Notes in Math., 181, 179-264. Zbl0687.35069MR992649
  3. [3] A. BENDALI, J.-M. DOMINGUEZ, S. GALLIC, 1985, Variational Approach for the Vector Potential Formulation of the Stokes and Navier-Stokes Problems in Three Dimensional Domains, J. Math. Anal, and Appl., 107, 537-560. Zbl0591.35053MR787732
  4. [4] J. H. BRAMBLE, J. E. PASCIAK, A. H. SCHATZ, 1986, The construction of Preconditioners for Elliptic Problems by Substructuring, I, Math. Comp. 47, 103-134. Zbl0615.65112MR842125
  5. [5] J. H. BRAMBLE, J. E. PASCIAK, J. Xu, 1991, Analysis of Multigrid Algorithms with Non-nested Spaces or Non-inherited Quadratic Forms, Math. Comp., 56, 389-414. Zbl0699.65075
  6. [6] P. G. ClARLET, 1978, The Finite Element Method in Elliptic Problems, North-Holland, Amsterdam, 1978. Zbl0383.65058
  7. [7] J.-M DOMINGUEZ, 1983, Formulations en Potential Vecteur du système de Stokes dans un Domaine de R3, Pub. lab. An.Num., L.A., 189, Univ. Paris VI. 
  8. [8] K. O. FRIEDRICHS, 1955, Differential forms on Riemannian Manifolds, Comm. Pure Appl. Math., 8, 551-590. Zbl0066.07504MR87763
  9. [9] V. GEORGESCU, 1979, Some Boundary Value Problem for Differential Formson Compact Riemannian Manifolds, Ann. Mat. Para Appl., 122, 159-198. Zbl0432.58026MR565068
  10. [10] V. GIRAULT, 1988, Incompressible Finite Element Methods for Navier-Stokes equations with Nonstandard Boundary Conditions in R3, Math. Comp., 51, 55-74. Zbl0666.76053MR942143
  11. [11] V. GIRAULT, P.-A. RAVIART, 1986, Finite Element Methods for Navier-Stokes Equations, Springer Series in Computational Mathematics, Springer-Verlag. Zbl0585.65077MR851383
  12. [12] P. LEE, 1990, On the Vector-Scalar Potential Formulation of the Three Dimensional Eddy Current Problem, Thesis, Cornell University. 
  13. [13] P. LEE, 1993, A Lagrange Multiplier Method for the Interface Equations from Electromagnetic Applications, SIAM J. Numer. Anal,, 30, 478-507. Zbl0773.65084MR1211401
  14. [14] J.-L. LIONS, E. MAGENES, 1972, Non-homogeneous Boundary Value Problemsand Applications, I, Springer. Zbl0223.35039
  15. [15] P. NEITTAANMAKI, J. SARANEN, 1980, Finite Element Approximation of Electromagnetic Fields in Three Dimensional Space, Numer. Funct. Anal. Optimiz., 2, 487-506. Zbl0451.65087MR605756
  16. [16] R. VERFURTH, 1987, Mixed Finite Element Approximation of the Vector Potential, Numer. Math., 50, 685-695. Zbl0596.76073MR884295
  17. [17] R. TEMAM, 1984, Navier-Stokes Equations, North-Holland. Zbl0568.35002MR769654

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