Convergence of a finite element discretization of the Navier-Stokes equations in vorticity and stream function formulation

Mohamed Amara; Christine Bernardi

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 5, page 1033-1056
  • ISSN: 0764-583X

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Amara, Mohamed, and Bernardi, Christine. "Convergence of a finite element discretization of the Navier-Stokes equations in vorticity and stream function formulation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.5 (1999): 1033-1056. <http://eudml.org/doc/193953>.

@article{Amara1999,
author = {Amara, Mohamed, Bernardi, Christine},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {improved convergence; Stokes equations; stream function and vorticity formulation; well-posedness; mortar element discretization; higher-order discretizations; Navier-Stokes equations; affine finite elements; a priori error estimates},
language = {eng},
number = {5},
pages = {1033-1056},
publisher = {Dunod},
title = {Convergence of a finite element discretization of the Navier-Stokes equations in vorticity and stream function formulation},
url = {http://eudml.org/doc/193953},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Amara, Mohamed
AU - Bernardi, Christine
TI - Convergence of a finite element discretization of the Navier-Stokes equations in vorticity and stream function formulation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 5
SP - 1033
EP - 1056
LA - eng
KW - improved convergence; Stokes equations; stream function and vorticity formulation; well-posedness; mortar element discretization; higher-order discretizations; Navier-Stokes equations; affine finite elements; a priori error estimates
UR - http://eudml.org/doc/193953
ER -

References

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  1. [1] M. Amara, M. Ben Youne and C. Bernardi, Error indicators for the Navier-Stokes equations in stream function and vorticity formulation. Numer. Math. 80 (1998) 181-206. Zbl0914.76046MR1645033
  2. [2] M. Amara and F. El Dabaghi, An optimal C0 finite element algorithm for the 2D biharmonic problem: theoretical analysis and numerical results. Numer. Math. (submitted). Zbl0997.65133
  3. [3] M. Ben Younes, Méthodes d'éléments finis avec joints pour le problème de Stokes en formulation fonction courant - tourbillon. Ph. D. thesis, Université Pierre et Marie Curie, France (1997). 
  4. [4] C. Bernardi and V. Girault, A local regularization operator for triangular and quadrilateral finite elements. SIAM J. Numer. Anal. 35 (1998) 1893-1916. Zbl0913.65007MR1639966
  5. [5] C. Bernardi, V. Girault and Y. Maday, Mixed spectral element approximation of the Navier-Stokes equations in the stream-function and vorticity formulation. IMA J. Numer. Anal. 12 (1992) 565-608. Zbl0753.76130MR1186736
  6. [6] C. Bernardi and Y. Maday, Mesh adaptivity in finite elements by the mortar method. Internal Report 94029, Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, France (1994). Zbl0954.65081
  7. [7] C. Bernardi, Y. Maday and A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method, in Collège de France Seminar XI, H. Brezis and J.-L. Lions Eds., Pitman (1994) 13-51. Zbl0797.65094MR1268898
  8. [8] F. Brezzi, J. Rappaz and P.-A. Raviart, Finite dimensional approximation of nonlinear problems, Part I: Branches of nonsingular solutions. Numer. Math. 36 (1980) 1-25. Zbl0488.65021MR595803
  9. [9] P.G. Ciarlet, Basic Error Estimates for Elliptic Problems, in Handbook of Numerical Analysis, Vol. II, P.G. Ciarlet and J.-L. Lions Eds., North-Holland (1991). Zbl0875.65086MR1115237
  10. [10] M. Dauge, Neumann and mixed problems on curvilinear polyhedra. Integral Equations Operator Theory 15 (1992) 227-261. Zbl0767.46026MR1147281
  11. [11] V. Girault and P.-A. Raviart, An analysis of a mixed finite element method for the Navier-Stokes equations. Numer. Math. 33 (1979) 235-271. Zbl0396.65070MR553589
  12. [12] V. Girault and P.-A. Raviart, Finite Element Methods for the Navier-Stokes Equations, Theory and Algorithms. Springer-Verlag (1986). Zbl0585.65077MR851383
  13. [13] R. Glowinski and O. Pironneau, Numerical methods for the first biharmonic equation and for the two-dimensional Stokes problem. SIAM Rev. 21 (1979) 167-212. Zbl0427.65073MR524511
  14. [14] P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman (1985). Zbl0695.35060MR775683
  15. [15] R. Scholz, A mixed method for fourth order problems using linear finite elements. RAIRO Anal. Numér. 12 (1978) 85-90. Zbl0382.65059MR483557

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