Abstract
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.
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References
Belytschko T., Lu Y. Y. and Gu L. (1994) Element-free Galerkin methods. Int. J. Num. Meth. Engrg. 37, 229–256
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, 111–126
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, 3–47
Belytschko T., Organ D. and Krongauz Y. (1995) A coupled finite element-free Galerkin method. Comput. Mech. 17, 186–195
Bonet J. and Kulasegaram S. (1999) Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Comp. Meth. Appl. Mech. Engrg. 180, 97–115
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, 259
Hegen D. (1996) Element Free Galerkin methods in combination with finite element approaches. Comp. Meth. Appl. Mech. Engrg. 135, 143–166
Huerta A. and Fernandez-Méndez S. (2001) Enrichment and coupling of the finite element method and meshless methods. Int. J. Num. Meth. Engrg., 48, 1615–1636
Huerta A. and Fernandez-Méndez S. (2001) Time accurate consistently stabilized mesh-free methods for convection dominated problems. Int. J. Num. Meth. Engrg., submitted
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, 153–170
Liu W.K., Belytschko T. and Oden J.T. eds. (1996) Meshless Methods. Comput. Meth. Appl. Mech. Engrg. 139
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, 113–154
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Fernández-Méndez, S., Huerta, A. (2003). Coupling Finite Elements and Particles for Adaptivity: An Application to Consistently Stabilized Convection-Diffusion. In: Griebel, M., Schweitzer, M.A. (eds) Meshfree Methods for Partial Differential Equations. Lecture Notes in Computational Science and Engineering, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56103-0_9
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DOI: https://doi.org/10.1007/978-3-642-56103-0_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43891-5
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