Enrichment and coupling of the finite element and meshless methods
A mixed hierarchical approximation based on finite elements and meshless methods is presented. Two cases are considered. The first one couples regions where finite elements or meshless methods are used to interpolate: continuity and consistency is preserved. The second one enriches a finite element...
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| Vydáno v: | International journal for numerical methods in engineering Ročník 48; číslo 11; s. 1615 - 1636 |
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| Hlavní autoři: | , |
| Médium: | Journal Article Publikace |
| Jazyk: | angličtina |
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Chichester, UK
John Wiley & Sons, Ltd
20.08.2000
Wiley and Sons Wiley |
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| ISSN: | 0029-5981, 1097-0207 |
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| Abstract | A mixed hierarchical approximation based on finite elements and meshless methods is presented. Two cases are considered. The first one couples regions where finite elements or meshless methods are used to interpolate: continuity and consistency is preserved. The second one enriches a finite element mesh with particles. Thus, there is no need to remesh in adaptive refinement processes. In both cases the same formulation is used, convergence is studied and examples are shown. Copyright © 2000 John Wiley & Sons, Ltd. |
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| AbstractList | A mixed hierarchical approximation based on finite elements and meshless methods is presented. Two cases are considered. The first one couples regions where finite elements or meshless methods are used to interpolate: continuity and consistency is preserved. The second one enriches a finite element mesh with particles. Thus, there is no need to remesh in adaptive refinement processes. In both cases the same formulation is used, convergence is studied and examples are shown. Copyright © 2000 John Wiley & Sons, Ltd. A mixed hierarchical approximation based on finite elements and meshless methods is presented. Two cases are considered. The first one couples regions where finite elements or meshless methods are used to interpolate: continuity and consistency is preserved. The second one enriches a finite element mesh with particles. Thus, there is no need to remesh in adaptive refinement processes. In both cases the same formulation is used, convergence is studied and examples are shown. Peer Reviewed A mixed hierarchical approximation based on finite elements and meshless methods is presented. Two cases are considered. The first one couples regions where finite elements or meshless methods are used to interpolate: continuity and consistency is preserved. The second one enriches a finite element mesh with particles. Thus, there is no need to remesh in adaptive refinement processes. In both cases the same formulation is used, convergence is studied and examples are shown. |
| Author | Fernández-Méndez, Sonia Huerta, Antonio |
| Author_xml | – sequence: 1 givenname: Antonio surname: Huerta fullname: Huerta, Antonio email: antonio.huerta@upc.es organization: Departament de Matemàtica Aplicada III, E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universitat Politècnica de Catalunya, Campus Nord, E-08034 Barcelona, Spain – sequence: 2 givenname: Sonia surname: Fernández-Méndez fullname: Fernández-Méndez, Sonia organization: Departament de Matemàtica Aplicada III, E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universitat Politècnica de Catalunya, Campus Nord, E-08034 Barcelona, Spain |
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| Cites_doi | 10.1002/fld.1650211010 10.1002/nme.1620370205 10.1016/S0045-7825(99)00071-7 10.1007/BF00364080 10.1002/fld.1650200824 10.1007/BF02736130 10.1007/BF00369940 10.1115/1.2788993 10.1002/(SICI)1097-0207(19960330)39:6<923::AID-NME887>3.0.CO;2-W 10.1016/S0045-7825(96)90021-3 10.1002/(SICI)1099-1484(200002)5:2<87::AID-CFM86>3.0.CO;2-W 10.1016/0045-7825(94)90056-6 10.1002/(SICI)1097-0207(19991210)46:10<1803::AID-NME725>3.0.CO;2-3 10.1142/S0218202599000117 10.1016/0045-7825(96)00994-2 10.1016/S0045-7825(96)01078-X 10.1016/S0045-7825(96)01132-2 |
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| Contributor | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
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| Copyright | Copyright © 2000 John Wiley & Sons, Ltd. info:eu-repo/semantics/openAccess Attribution |
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| Issue | 11 |
| Keywords | meshless method h-p refinement adaptivity finite element method mixed interpolation convergence |
| Language | English |
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| References | Organ D, Fleming M, Terry T, Belytschko T. Continuous meshless approximations for nonconvex bodies by diffraction and transparency. Computational Mechanics 1996; 18:225-235. Belytschko T, Tabbara M. Dynamic fracture using element-free galerkin methods. International Journal for Numerical Methods in Engineering 1996; 39:923-938. Liu WK, Chen Y. Wavelet and multiple scale reproducing kernel methods. International Journal for Numerical Methods in Fluids 1995; 21:901-931. Fernández-Méndez S, Díez P, Huerta A. Convergence of finite elements enriched with meshless methods. SIAM Journal of Numerical Analysis, submitted. Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P. Meshless methods: an overview and recent developments. Computer Methods in Applied Mechanics and Engineering 1996; 139:3-47. Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256. Liu WK, Chen Y, Jun S, Chen JS, Belytschko T, Pan C, Uras RA, Chang CT. Overview and applications of the reproducing Kernel particle methods. Archives of Computational Methods in Engineering, State of the Art Reviews 1996; 3:3-80. Lu YY, Belytschko T, Gu L. A new implementation of the element free Galerkin method. Computer Methods in Applied Mechanics and Engineering 1994; 113:397-414. Hegen D. Element free Galerkin methods in combination with finite element approaches. Computer Methods in Applied Mechanics and Engineering 1996; 135:143-166. Liu WK, Jun S, Zhang YF. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids 1995; 20:1081-1106. Huerta A, Díez P. Error estimation including pollution assessment for nonlinear finite element analysis. Computer Methods in Applied Mechanics and Engineering 2000; 181:21-41. Díez P, Arroyo M, Huerta A. Adaptivity based on error estimation for viscoplastic softening materials. Mechanics of Cohesive-Frictional Materials 2000; 5:87-112. Liu WK, Belytschko T, Oden JT (eds), Meshless methods. Computer Methods in Applied Mechanics and Engineering 1996; 139:1-440. Liu WK, Uras RA, Chen Y. Enrichment of the finite element method with reproducing Kernel particle method. Journal of Applied Mechanics 1997; 64:861-870. Liu WK, Li S, Belytschko T. Moving least square reproducing kernel methods. (I) Methodology and convergence. Computer Methods in Applied Mechanics and Engineering 1997; 143:113-154. Vila JP. On particle weighted methods and smooth particle hydrodynamics. Mathematical Models and Methods in Applied Sciences 1999; 9:161-209. Huerta A, Rodríguez-Ferran A, Díez P, Sarrate J. Adaptive finite element strategies based on error analysis. International Journal for Numerical Methods in Engineering 1999; 46:1803-1818. Belytschko T, Organ D, Krongauz Y. A coupled finite element-free Galerkin method. Computational Mechanics 1995; 17:186-195. 1995; 20 1994; 113 1996; 18 1996; 39 1995; 17 2000; 5 1997; 64 1997; 143 1995; 21 1998 1999; 46 1997 1994; 37 1996; 135 1996; 3 1996; 139 1999; 9 2000; 181 Belytschko (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB3) 1994; 37 Huerta (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB20) 2000; 181 Huerta (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB21) 1999; 46 Fern ndez-M ndez (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB18) Liu (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB14) 1997; 64 Organ (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB8) 1996; 18 Vila (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB10) 1999; 9 Liu (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB16) 1997; 143 Liu (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB2) 1995; 20 Belytschko (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB6) 1996; 39 Huerta (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB17) Hegen (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB13) 1996; 135 Liu (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB1) 1995; 21 Liu (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB12) 1996; 3 Lu (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB7) 1994; 113 Belytschko (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB5) 1995; 17 Liu (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB15) 1996; 139 D ez (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB19) 2000; 5 Belytschko (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB4) 1997 Kulasegaram (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB9) 1998 Belytschko (10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S-BIB11) 1996; 139 |
| References_xml | – reference: Liu WK, Chen Y, Jun S, Chen JS, Belytschko T, Pan C, Uras RA, Chang CT. Overview and applications of the reproducing Kernel particle methods. Archives of Computational Methods in Engineering, State of the Art Reviews 1996; 3:3-80. – reference: Huerta A, Díez P. Error estimation including pollution assessment for nonlinear finite element analysis. Computer Methods in Applied Mechanics and Engineering 2000; 181:21-41. – reference: Liu WK, Uras RA, Chen Y. Enrichment of the finite element method with reproducing Kernel particle method. Journal of Applied Mechanics 1997; 64:861-870. – reference: Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P. Meshless methods: an overview and recent developments. Computer Methods in Applied Mechanics and Engineering 1996; 139:3-47. – reference: Belytschko T, Organ D, Krongauz Y. A coupled finite element-free Galerkin method. Computational Mechanics 1995; 17:186-195. – reference: Hegen D. Element free Galerkin methods in combination with finite element approaches. Computer Methods in Applied Mechanics and Engineering 1996; 135:143-166. – reference: Liu WK, Jun S, Zhang YF. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids 1995; 20:1081-1106. – reference: Belytschko T, Tabbara M. Dynamic fracture using element-free galerkin methods. International Journal for Numerical Methods in Engineering 1996; 39:923-938. – reference: Lu YY, Belytschko T, Gu L. A new implementation of the element free Galerkin method. Computer Methods in Applied Mechanics and Engineering 1994; 113:397-414. – reference: Huerta A, Rodríguez-Ferran A, Díez P, Sarrate J. Adaptive finite element strategies based on error analysis. International Journal for Numerical Methods in Engineering 1999; 46:1803-1818. – reference: Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256. – reference: Díez P, Arroyo M, Huerta A. Adaptivity based on error estimation for viscoplastic softening materials. Mechanics of Cohesive-Frictional Materials 2000; 5:87-112. – reference: Liu WK, Li S, Belytschko T. Moving least square reproducing kernel methods. (I) Methodology and convergence. Computer Methods in Applied Mechanics and Engineering 1997; 143:113-154. – reference: Fernández-Méndez S, Díez P, Huerta A. Convergence of finite elements enriched with meshless methods. SIAM Journal of Numerical Analysis, submitted. – reference: Liu WK, Belytschko T, Oden JT (eds), Meshless methods. Computer Methods in Applied Mechanics and Engineering 1996; 139:1-440. – reference: Vila JP. On particle weighted methods and smooth particle hydrodynamics. Mathematical Models and Methods in Applied Sciences 1999; 9:161-209. – reference: Liu WK, Chen Y. Wavelet and multiple scale reproducing kernel methods. International Journal for Numerical Methods in Fluids 1995; 21:901-931. – reference: Organ D, Fleming M, Terry T, Belytschko T. Continuous meshless approximations for nonconvex bodies by diffraction and transparency. 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| SubjectTerms | Adaptivity Anàlisi numèrica Convergence Elements finits, Mètode dels Engineering Sciences Finite element method h-p refinement Matemàtiques i estadística Mechanics Meshless method Mixed interpolation Mètodes en elements finits Àrees temàtiques de la UPC |
| Title | Enrichment and coupling of the finite element and meshless methods |
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