Coupling Finite Elements and Particles for Adaptivity: An Application to Consistently Stabilized Convection-Diffusion

  • Sonia Fernández-Méndez
  • Antonio Huerta
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 26)


A mixed approximation coupling finite elements and mesh-less methods is presented. It allows selective refinement of the finite element solution without remeshing cost. The distribution of particles can be arbitrary. Continuity and consistency is preserved. The behaviour of the mixed interpolation in the resolution of the convection-diffusion equation is analyzed.


Meshless Method Finite Element Solution Meshfree Method Element Free Galerkin Method Reproduce Kernel Particle Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Belytschko T., Lu Y. Y. and Gu L. (1994) Element-free Galerkin methods. Int. J. Num. Meth. Engrg. 37, 229–256MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Belytschko T., Krongauz Y., Fleming M., Organ D. and Liu W.K. (1996) Smoothing and accelerated computations in the element free galerkin method. J. Comp. Appl. Math. 74, 111–126MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Belytschko T., Krongauz Y., Organ D., Fleming M. and Krysl P. (1996) Meshless Methods: an Overview and Recent Developments. Comp. Meth. Appl. Mech. Engrg. 139, 3–47zbMATHCrossRefGoogle Scholar
  4. 4.
    Belytschko T., Organ D. and Krongauz Y. (1995) A coupled finite element-free Galerkin method. Comput. Mech. 17, 186–195MathSciNetzbMATHGoogle Scholar
  5. 5.
    Bonet J. and Kulasegaram S. (1999) Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Comp. Meth. Appl. Mech. Engrg. 180, 97–115zbMATHCrossRefGoogle Scholar
  6. 6.
    Brooks A.N. and Hugues T. (1982) Streamline upwind/petrov-galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier-stokes equations. Comput. Meth. Appl. Mech. Engrg. 32, 259CrossRefGoogle Scholar
  7. 7.
    Hegen D. (1996) Element Free Galerkin methods in combination with finite element approaches. Comp. Meth. Appl. Mech. Engrg. 135, 143–166zbMATHCrossRefGoogle Scholar
  8. 8.
    Huerta A. and Fernandez-Méndez S. (2001) Enrichment and coupling of the finite element method and meshless methods. Int. J. Num. Meth. Engrg., 48, 1615–1636CrossRefGoogle Scholar
  9. 9.
    Huerta A. and Fernandez-Méndez S. (2001) Time accurate consistently stabilized mesh-free methods for convection dominated problems. Int. J. Num. Meth. Engrg., submittedGoogle Scholar
  10. 10.
    Jansen K.E., Collins S.S., Whiting C. and Shakib F. (1999), A better consistency for low-order stabilized finite element methods. Comput. Meth. Appl. Mech. Engrg. 174, 153–170zbMATHCrossRefGoogle Scholar
  11. 11.
    Liu W.K., Belytschko T. and Oden J.T. eds. (1996) Meshless Methods. Comput. Meth. Appl. Mech. Engrg. 139 Google Scholar
  12. 12.
    Liu W.K., Li S. and Belytschko T. (1997) Moving least square reproducing kernel methods. (I) Methodology and convergence. Comput. Methods Appl. Mech. Engrg. 143, 113–154MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Sonia Fernández-Méndez
    • 1
  • Antonio Huerta
    • 1
  1. 1.Departament de Matemàtica Aplicada III, E.T.S. de Ingenieros de CaminosUniversitat Politècnica de CatalunyaBarcelonaSpain

Personalised recommendations