Pseudo-divergence-free element free Galerkin method for incompressible fluid flow

Computer Methods in Applied Mechanics and Engineering

Volumn 193, Issue 12-14, 2004, Pages 1119-1136

  Huerta, Antonio ^a   Vidal, Yolanda ^a   Villon, Pierre ^b  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

Diffuse derivatives; Element free Galerkin; Incompressible flow; LBB condition; Locking; Moving least squares

Indexed keywords

FINITE ELEMENT METHOD; GALERKIN METHODS; INCOMPRESSIBLE FLOW; INTERPOLATION; PROBLEM SOLVING;

DIVERGENCE-FREE SPACE; MESH-FREE METHODS;

FLOW OF FLUIDS;

FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW;

EID: 1842526870     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2003.12.010     Document Type: Article

References (34)

1. Girault V. Raviart P.-A. Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms 1986 Springer-Verlag Berlin
2. P.M. Gresho, R.L. Sani, Incompressible Flow and the Finite Element Method, vol. 1: Advection Diffusion, vol. 2: Isothermal Laminar Flow, John Wiley - Sons, Chichester, 2000
3. Gunzburger M.D. Finite Element Methods for Viscous Incompressible Flows. A Guide to Theory, Practice, and Algorithms 1989 Academic Press Boston, MA
4. Pironneau O. Finite Element Methods for Fluids 1989 John Wiley - Sons Chichester
5. Quartapelle L. Numerical solution of the incompressible Navier-Stokes equations International Series of Numerical Mathematics vol. 113 1993 Birkhäuser-Verlag Basel
6. Quarteroni A. Valli A. Numerical approximation of partial differential equations Springer Series in Computational Mathematics vol. 23 1994 Springer-Verlag Berlin
7. Temam R. Navier-Stokes Equations. Theory and Numerical Analysis 2001 AMS Chelsea Publishing Providence, RI Corrected reprint of the 1984 edition, North-Holland, Amsterdam, 1984
8. Donea J. Huerta A. Finite Element Methods for Flow Problems 2003 John Wiley - Sons Chichester
9. Malkus D.S. Eigenproblems associated with the discrete LBB condition for incompressible finite elements Int. J. Engrg. Sci. 19 10 1981 1299-1310
10. Brezzi F. Fortin M. Mixed and hybrid finite element methods Springer Series in Computational Mathematics vol. 15 1991 Springer-Verlag New York
11. Chapelle D. Bathe K.-J. The inf-sup test Comput. Struct. 47 4-5 1993 537-545
12. Bathe K.-J. Hendriana D. Brezzi F. Sangalli G. Inf-sup testing of upwind methods Int. J. Numer. Methods Engrg. 48 5 2000 745-760
13. Zhu T. Atluri S.N. A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method Comput. Mech. 21 3 1998 211-222
14. Dolbow J. Belytschko T. Volumetric locking in the element free Galerkin method Int. J. Numer. Methods Engrg. 46 6 1999 925-942
15. Askes H. de Borst R. Heeres O. Conditions for locking-free elasto-plastic analyses in the element-free Galerkin method Comput. Methods Appl. Mech. Engrg. 173 1-2 1999 99-109
16. Chen J.S. Yoon S. Wang H. Liu W.K. An improved reproducing kernel particle method for nearly incompressible finite elasticity Comput. Methods Appl. Mech. Engrg. 181 1-3 2000 117-145
17. Hughes T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis 2000 Dover Publications Inc. New York Corrected reprint of the 1987 original, Prentice-Hall Inc., Englewood Cliffs, NJ
18. Huerta A. Fernández-Méndez S. Locking in the incompressible limit for the element free Galerkin method Int. J. Numer. Methods Engrg. 51 11 2001 1361-1383
19. Nayroles B. Touzot G. Villon P. Generating the finite element method: diffuse approximation and diffuse elements Comput. Mech. 10 5 1992 307-318
20. P. Villon, Contribution à l'optimisation, Thèse présentée pour l'obtention du grade de docteur d'état, Université de Technologie de Compiègne, Compiègne, France, 1991
21. Vidal Y. Villon P. Huerta A. Locking in the incompressible limit: pseudo-divergence-free element-free Galerkin Rev. Eur. Éléments Finis 11 7/8 2002 869-892
22. Vidal Y. Villon P. Huerta A. Locking in the incompressible limit: pseudo-divergence-free element-free Galerkin Commun. Numer. Methods Engrg. 19 9 2003 725-735
23. W.K. Liu, T. Belytschko, J.T. Oden (Eds.), Meshless methods, Comput. Methods Appl. Mech. Engrg. 139 (1-4) (1996) 1-440
24. Fernández-Méndez S. Huerta A. Coupling finite elements and particles for adaptivity: an application to consistently stabilized convection-diffusion Griebel M. Schweitzer M.A. Meshfree Methods for Partial Differential Equations Lecture Notes in Computational Science and Engineering vol. 26 2002 117-129 Springer-Verlag Berlin papers from the International workshop, Universität Bonn, Germany, September 11-14, 2001
25. S. Fernández-Méndez, P. Díez, A. Huerta, Convergence of finite elements enriched with meshless methods, Numer. Math., DOI: 10.1007/s00211-003-0465-x 10.1007/s00211-003-0465-x
26. Belytschko T. Krongauz Y. Fleming M. Organ D. Liu W.K. Smoothing and accelerated computations in the element free Galerkin method J. Comput. Appl. Math. 74 1-2 1996 111-126
27. Huerta A. Fernández-Méndez S. Díez P. Enrichissement des interpolations d'éléments finis en utilisant des méthodes de particules ESAIM--Math. Model. Numer. Anal. 36 6 2002 1027-1042
28. Stenberg R. On some techniques for approximating boundary conditions in the finite element method J. Comput. Appl. Math. 63 1-3 1995 139-148
29. Arnold D.N. Brezzi F. Cockburn B. Marini L.D. Unified analysis of discontinuous Galerkin methods for elliptic problems SIAM J. Numer. Anal. 39 5 2001/2002 1749-1779
30. Babuska I. Banerjee U. Osborn J.E. Meshless and generalized finite element methods: a survey of some major results Griebel M. Schweitzer M.A. Meshfree Methods for Partial Differential Equations Lecture Notes in Computational Science and Engineering vol. 26 2002 1-20 Springer-Verlag Berlin papers from the International workshop, Universität Bonn, Germany, September 11-14, 2001
31. Becker R. Mesh adaptation for Dirichlet flow control via Nitsche's method Commun. Numer. Methods Engrg. 18 9 2002 669-680
32. S. Fernández-Méndez, A. Huerta, Imposing essential boundary conditions in mesh-free methods, Comput. Methods Appl. Mech. Engrg. 193 (12-14) (2004), doi:10.1016/j.cma.2003.12.019 doi:10.1016/j.cma.2003.12.019
33. Griebel M. Schweitzer M.A. A particle-partition of unity method. Part V: Boundary conditions Hildebrandt S. Karcher H. Geometric Analysis and Nonlinear Partial Differential Equations 2002 517-540 Springer Berlin
34. Oden J.T. Jacquotte O.-P. Stability of some mixed finite element methods for Stokesian flows Comput. Methods Appl. Mech. Engrg. 43 2 1984 231-247