Praveen

May 5, 2004 02:35 
Re: Meshless FD method over FEM?
Here is a list of references on meshless methods in CFD. There is a growing body of literature in structural mechanics, see IJNME, JNMF, and Comp. Meth. Appl. Mech. Engg.
<h3> Some references on Meshless Methods </h3>  T Liszka, "An interpolation method for an irregular net of nodes", Int. Jl. for Num. Meth. in Engg., 20:15991612, 1984.
 T Liszka and J Orkisz, "The finite difference method at arbitrary irregular grids and its application in applied mechanics'', Comp. Struct., 11:8395, 1980.
 KC Chung, "A generalised finite difference method for heat transfer problems of irregular geometries'', Num. Heat Transfer, 4:345357, 1981.
 EJ Kansa (1990): "Multiquadrics A scattered data approximation scheme with applications to computational fluid dynamics: II. Solutions to parabolic, hyperbolic and elliptic partial differential equations", Comput. Math. Appl., 19(68):147161.
 JT Batina, "A gridless Euler/NavierStokes solution algorithm for complex aircraft applications'', AIAA Paper 930333, 1993.
 T Belytschko, YY Lu, and L Gu, "Elementfree Galerkin methods", Int. Jl. Num. Meth. Engg., 37:229256, 1994.
 AK Ghosh, SM Deshpande, "Least squares kinetic upwind method for inviscid compressible flows'', AIAA paper 951735,1995.
 Yagawa G and Yamada T, "Free mesh method: A new meshless finite element method'', Comp. Mech., 18:383386, 1996.
 T Belytschko, Y Krongauz, D Organ, M Flemming and P Krysl, "Meshless methods: An overview and recent developments", Comput. Methods Appl. Mech. Engg., Vol. 139, pp. 347, 1996. (This contains a comprehensive review of many meshless techniques.)
 K Morinishi (1999): "An implicit gridless type solver for the NavierStokes equations'', Int. Symp. on CFD, Bremen.
 H Wendland (1999): "Meshless Galerkin methods using radial basis functions", Math. Comp., 68:15211531.
 M Junk, "Do finite volume methods really need a mesh ?", Int. Workshop on Meshfree Methods for PDE, Bonn, September, 2001.
 R Lohner, C Sacco, E Onate and S Idelsohn (2002): "A finite point method for compressible flows'', Int. Jl. Num. Meth. Engg., Vol. 53, pp. 17651779.
 Michael Griebel and Marc Schweitzer, ed. (2002): Meshfree methods for Partial Differential Equations, LNCSE, Springer, 2002.
 G.R. Liu: Meshfree Methods  Moving beyond the Finite Element Method , 712 pages, 2002, CRC Press. ISBN: 0849312388. (This is the first textbook on meshless methods, and till now the only one that I am aware of.)
