Element-free Galerkin method: Convergence of the continuous and discontinuous shape functions

Duarte, 1995, A review of some meshless methods to solve partial differential equations Liszka, 1980, The finite difference method at arbitrary irregular grids and its applications in applied mechanics, Comput. Struct., 11, 83, 10.1016/0045-7949(80)90149-2 Monaghan, 1982, An introduction to SPH, Comput. Phys. Commun., 48, 89, 10.1016/0010-4655(88)90026-4 Nayroles, 1992, Generalizing the finite element method: diffuse approximation and diffuse elements, Comput. Mech., 10, 307, 10.1007/BF00364252 Kansa, 1990, Multiquadrics — a scattered data approximation scheme with applications to computational fluid dynamics: I. Surface approximations and partial derivative estimates, Comput. Math. Applic., 19, 127, 10.1016/0898-1221(90)90270-T 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. Applic., 19, 147, 10.1016/0898-1221(90)90271-K Belytschko, 1994, Element-free Galerkin methods, Int. J. Numer. Methods Engrg., 37, 229, 10.1002/nme.1620370205 Qian, 1993, Wavelet and the numerical solution of partial differential equations, J. Comput. Phys., 106, 155, 10.1006/jcph.1993.1100 Duarte, 1995, Hp clouds — A meshless method to solve boundary-value problems Liu, 1995, Reproducing kernel particle methods for structural dynamics, Int. J. Numer. Methods Engrg., 38, 1655, 10.1002/nme.1620381005 Babuška, 1995, The partition of unity finite element method, 10.21236/ADA301760 Babuška, 1997, The partition of unity finite element method, Int. J. Numer. Methods Engrg., 40, 727, 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.3.CO;2-E Krysl, 1996, Analysis of thin shells by the Element-Free Galerkin method, Int. J. Solids Struct., 33, 3057, 10.1016/0020-7683(95)00265-0 Krysl, 1996, Analysis of thin plates by the Element-Free Galerkin method, Comput. Mech., 17, 26, 10.1007/BF00356476 Cleveland, 1993 Lancaster, 1986 Belytschko, 1995, A coupled finite element-element-free Galerkin method, Comput. Mech., 17, 186, 10.1007/BF00364080 Krongauz, 1996, Enforcement of essential boundary conditions in meshless approximations using finite elements, Comput, Methods Appl. Mech. Engrg., 131, 133, 10.1016/0045-7825(95)00954-X Stummel, 1979, The generalized patch test, SIAM J. Numer. Anal., 3, 449, 10.1137/0716037 Strang, 1973 Lancaster, 1981, Surfaces generated by moving least squares methods, Math. Comput., 37, 141, 10.1090/S0025-5718-1981-0616367-1 Organ, 1996, Continuous meshless approximations for nonconvex bodies by diffraction and transparency, Comput. Mech., 18, 225, 10.1007/BF00369940 Ciarlet, 1991, Basic error estimates for elliptic problem, Vol. II Brenner, 1994 Liu, 1997, Reproducing least square kernel Galerkin method. (i) Methodology and convergence, Comput. Methods Appl. Mech. Engrg., 143, 113, 10.1016/S0045-7825(96)01132-2 Belytschko, 1996, Smoothing and accelerated computations in the element-free Galerkin method, J. Comput. Appl. Math., 74, 111, 10.1016/0377-0427(96)00020-9 Grisvard, 1985 Babuška, 1972, A finite element scheme for domains with corners, Numer. Math., 20, 1, 10.1007/BF01436639 Babǔska, 1979, Direct and inverse error estimates for finite element with mesh refinements, Numer. Math., 33, 447, 10.1007/BF01399326 Babuška, 1981, Error estimates for the combined h and p versions of the finite element method, Numer. Math., 37, 257, 10.1007/BF01398256 Babuška, 1984, The post-processing approach in the finite element method — Part II. Calculation of stress intensity factors, Int. J. Numer. Methods Engrg., 20, 1111, 10.1002/nme.1620200611 Bourlard, 1992, Coefficients of the singularities for elliptic boundary value problems on domains with conical points. III: Finite element methods on polygonal domains, SIAM J. Numer. Anal., 29, 136, 10.1137/0729009 Wahlbin, 1991, Local behavior in finite element methods, Vol. II, 353 Dautray, 1988 Rektorys, 1980 Szabo, 1991