Imposing essential boundary conditions in mesh-free methods
Tóm tắt
Từ khóa
Tài liệu tham khảo
Belytschko, 1996, Meshless methods: an overview and recent developments, Comput. Methods Appl. Mech. Engrg., 139, 3, 10.1016/S0045-7825(96)01078-X
1996, Comput. Methods Appl. Mech. Engrg., 139, 1
Liu, 1996, Overview and applications of the reproducing kernel particle methods, Arch. Comput. Methods Engrg., 3, 3, 10.1007/BF02736130
Belytschko, 1994, Element free Galerkin methods, Int. J. Numer. Methods Engrg., 37, 229, 10.1002/nme.1620370205
Liu, 1995, Reproducing kernel particle methods, Int. J. Numer. Methods Fluids, 20, 1081, 10.1002/fld.1650200824
Bonet, 2000, Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations, Int. J. Numer. Methods Engrg., 47, 1189, 10.1002/(SICI)1097-0207(20000228)47:6<1189::AID-NME830>3.0.CO;2-I
Zhu, 1998, A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method, Comput. Mech., 21, 211, 10.1007/s004660050296
Griebel, 2002, A particle-partition of unity method. Part V: Boundary conditions, 517
Babuska, 2002, Meshless and generalized finite element methods: A survey of some major results, vol. 26, 1
Gosz, 1996, Admissible approximations for essential boundary conditions in the reproducing kernel particle method, Comput. Mech., 19, 120, 10.1007/BF02824850
Belytschko, 1995, A coupled finite element–element-free Galerkin method, Comput. Mech., 17, 186, 10.1007/BF00364080
Huerta, 2000, Enrichment and coupling of the finite element and meshless methods, Int. J. Numer. Methods Engrg., 48, 1615, 10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S
Babuska, 1973, The finite element method with Lagrange multipliers, Numer. Math., 20, 179, 10.1007/BF01436561
Brezzi, 1974, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge, 8, 129
Chen, 1996, Reproducing kernel particle methods for large deformation analysis of non-linear, Comput. Methods Appl. Mech. Engrg., 139, 195, 10.1016/S0045-7825(96)01083-3
Günter, 1998, Implementation of boundary conditions for meshless methods, Comput. Methods Appl. Mech. Engrg., 163, 205, 10.1016/S0045-7825(98)00014-0
Wagner, 2000, Hierarchical enrichment for bridging scales and meshfree boundary conditions, Int. J. Numer. Methods Engrg., 50, 507, 10.1002/1097-0207(20010130)50:3<507::AID-NME33>3.0.CO;2-B
Chen, 2003, A reproducing kernel method with nodal interpolation property, Int. J. Numer. Methods Engrg., 56, 935, 10.1002/nme.592
A. Huerta, S. Fernández-Méndez, W.K. Liu, A comparison of two formulations to blend finite elements and mesh-free methods, Comput. Methods Appl. Mech. Engrg., in this issue
A. Huerta, S. Fernández-Méndez, Coupling element free Galerkin and finite element methods, in: Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2000), 11–14 September, Barcelona, 2000, electronic publication ISBN: 84-89925-70-4
Fernández-Méndez, 2002, Coupling finite elements and particles for adaptivity: an application to consistently stabilized convection–diffusion, vol. 26, 117
Huerta, 2002, Enrichissement des interpolations d' éléments finis en utilisant des méthodes de particules, ESAIM––Math. Model. Numer. Anal., 36, 1027, 10.1051/m2an:2003004
Fernández-Méndez, 2003, Convergence of finite elements enriched with meshless methods, Numer. Math., 96, 43, 10.1007/s00211-003-0465-x
Babuska, 1973, The finite element method with penalty, Math. Comp., 27, 221, 10.1090/S0025-5718-1973-0351118-5
Arnold, 2002, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal., 39, 1749, 10.1137/S0036142901384162
Nitsche, 1970, Über ein variations zur lösung von dirichlet-problemen bei verwendung von teilräumen die keinen randbedingungen unterworfen sind, Abh. Math. Se. Univ., 36, 9, 10.1007/BF02995904
Becker, 2002, Mesh adaptation for dirichlet flow control via Nitsche's method, Commun. Numer. Methods Engrg., 18, 669, 10.1002/cnm.529
J. Freud, R. Stenberg, On weakly imposed boundary conditions for second order problems, in: Proceeding of the International Conference on Finite Elements in Fluids––New Trends and Applications, Venezia, 1995