A comparison of efficiency and error convergence of multiquadric collocation method and finite element method

[1]  R. L. Hardy Multiquadric equations of topography and other irregular surfaces , 1971 .

[2]  G. Fairweather Finite Element Galerkin Methods for Differential Equations , 1978 .

[3]  R. Franke Scattered data interpolation: tests of some methods , 1982 .

[4]  C. Micchelli Interpolation of scattered data: Distance matrices and conditionally positive definite functions , 1986 .

[5]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[6]  W. Madych,et al.  Multivariate interpolation and condi-tionally positive definite functions , 1988 .

[7]  Leszek Demkowicz,et al.  Toward a universal adaptive finite element strategy part 3. design of meshes , 1989 .

[8]  Leszek Demkowicz,et al.  Toward a universal h-p adaptive finite element strategy , 1989 .

[9]  E. Kansa MULTIQUADRICS--A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS-- II SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS , 1990 .

[10]  R. L. Hardy Theory and applications of the multiquadric-biharmonic method : 20 years of discovery 1968-1988 , 1990 .

[11]  R. E. Carlson,et al.  The parameter R2 in multiquadric interpolation , 1991 .

[12]  W. R. Madych,et al.  Miscellaneous error bounds for multiquadric and related interpolators , 1992 .

[13]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[14]  Ivo Babuska,et al.  The p and h-p Versions of the Finite Element Method, Basic Principles and Properties , 1994, SIAM Rev..

[15]  Robert Schaback,et al.  Error estimates and condition numbers for radial basis function interpolation , 1995, Adv. Comput. Math..

[16]  J. Oden,et al.  H‐p clouds—an h‐p meshless method , 1996 .

[17]  M. Golberg,et al.  Discrete projection methods for integral equations , 1996 .

[18]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[19]  Y. Hon,et al.  Multiquadric method for the numerical solution of a biphasic mixture model , 1997 .

[20]  Ching-Shyang Chen,et al.  A numerical method for heat transfer problems using collocation and radial basis functions , 1998 .

[21]  Benny Y. C. Hon,et al.  An efficient numerical scheme for Burgers' equation , 1998, Appl. Math. Comput..

[22]  S. Atluri,et al.  A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics , 1998 .

[23]  Carsten Franke,et al.  Solving partial differential equations by collocation using radial basis functions , 1998, Appl. Math. Comput..

[24]  Graeme Fairweather,et al.  The method of fundamental solutions for elliptic boundary value problems , 1998, Adv. Comput. Math..

[25]  M. Golberg Boundary integral methods : numerical and mathematical aspects , 1999 .

[26]  Kwok Fai Cheung,et al.  Multiquadric Solution for Shallow Water Equations , 1999 .

[27]  Robert Schaback,et al.  Improved error bounds for scattered data interpolation by radial basis functions , 1999, Math. Comput..

[28]  E. Kansa,et al.  Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations , 2000 .

[29]  Robert Schaback,et al.  Adaptive Interpolation by Scaled Multiquadrics , 2002, Adv. Comput. Math..

[30]  Benny Y. C. Hon,et al.  Compactly supported radial basis functions for shallow water equations , 2002, Appl. Math. Comput..

[31]  Y. C. Hon,et al.  Numerical comparisons of two meshless methods using radial basis functions , 2002 .

[32]  Bengt Fornberg,et al.  Stable Computation of Multiquadric Interpolants for All Values of the Shape Parameter , 2004 .

[33]  B. Fornberg,et al.  A numerical study of some radial basis function based solution methods for elliptic PDEs , 2003 .

[34]  E. Kansa,et al.  Exponential convergence and H‐c multiquadric collocation method for partial differential equations , 2003 .