A posteriori error estimation for extended finite elements by an extended global recovery

International Journal for Numerical Methods in Engineering

Volumn 76, Issue 8, 2008, Pages 1123-1138

  Duflot, Marc ^a   Bordas, Stéphane ^b  

^a CENAERO   (Belgium)

^b UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

A posteriori error estimation; Extended finite elements; Fracture mechanics; Global derivative recovery; Partition of unity enrichment; Three dimensional problems

Indexed keywords

BRITTLE FRACTURE; CONCENTRATION (PROCESS); DERIVATIVES; ERROR ANALYSIS; ESTIMATION; FINITE ELEMENT METHOD; FRACTURE MECHANICS; INDUSTRIAL APPLICATIONS; STRAIN; STRENGTH OF MATERIALS; THREE DIMENSIONAL;

A POSTERIORI ERROR ESTIMATION; EXTENDED FINITE ELEMENTS; GLOBAL DERIVATIVE RECOVERY; PARTITION OF UNITY ENRICHMENT; THREE-DIMENSIONAL PROBLEMS;

RECOVERY;

EID: 57849113081     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2332     Document Type: Article

References (43)

1. Melenk JM, Babuška I. The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering 1996; 139:289-314.
2. Babuška I, Melenk I. Partition of unity method. International Journal for Numerical Methods in Engineering 1997; 40(4):727-758.
3. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 1999; 45(5):601-620.
4. Strouboulis T, Babuška I, Copps K. The design and analysis of the generalized finite element method. Computer Methods in Applied Mechanics and Engineering 2000; 181:43-69.
5. Strouboulis T, Copps K, Babuška I. The generalized finite element method: an example of its implementation and illustration of its performance. International Journal for Numerical Methods in Engineering 2000; 47(8): 1401-1417.
6. Stolarska M, Chopp DL, Moës N, Belytschko T. Modelling crack growth by level sets and the extended finite element method. International Journal for Numerical Methods in Engineering 2001; 51(8):943-960.
7. Sukumar N, Moës N, Belytschko T, Moran B. Extended finite element method for three-dimensional crack modelling. International Journal for Numerical Methods in Engineering 2000; 48(11):1549-1570.
8. Moës N, Gravouil A, Belytschko T. Non-planar 3d crack growth by the extended finite element and level sets. Part I: mechanical model. International Journal for Numerical Methods in Engineering 2002: 53:2549-2568.
9. Gravouil A, Moës N, Belytschko T. Non-planar 3d crack growth by the extended finite element and level sets. Part II: level set update. International Journal for Numerical Methods in Engineering 2002; 53:2569-2586.
10. Sukumar N, Chopp DL, Moran B. Extended finite element method and fast marching method for three-dimensional fatigue crack propagation. Engineering Fracture Mechanics 2003; 70(1):29-48.
11. Chopp DL, Sukumar N. Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method. International Journal of Engineering Science 2003; 41(8):865-869.
12. Moës N, Belytschko T. Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics 2002; 69:813-834.
13. Daux C, Moës N, Dolbow J, Sukumar N, Belytschko T. Arbitrary branched and intersecting cracks with the extended finite element method. International Journal for Numerical Methods in Engineering 1999; 48(12): 1741-1760.
14. Sukumar N, Huang ZY, Prévost J-H, Suo Z. Partition of unity enrichment for bimaterial interface cracks. International Journal for Numerical Methods in Engineering 2004; 59:1075-1102.
15. Legrain G, Moës N, Verron E. Stress analysis around the crack tips in finite strain problems using the extended finite element method. International Journal for Numerical Methods in Engineering 2005; 63:290-314.
16. Rethoré J, Gravouil A, Combescure A. An energy-conserving scheme for dynamic crack growth using the extended finite element method. International Journal for Numerical Methods in Engineering 2005; 63:631-659.
17. Bordas S, Moran B. Enriched finite elements and level sets for damage tolerance assessment of complex structures. Engineering Fracture Mechanics 2006; 73:1176-1201.
18. Bordas S, Conley JG, Moran B, Gray J, Nichols E. A simulation-based design paradigm for complex cast components. Engineering with Computers 2007; 23(1):25-37.
19. Bordas S, Nguyen VP, Dunant C, Nguyen-Dang H, Guidoum A. An extended finite element library. International Journal for Numerical Methods in Engineering 2007; 71:703-732.
20. Dunant C, Nguyen P, Belgasmia M, Bordas S, Guidoum A, Nguyen-Dang H. Architecture trade-offs of including a mesher in an object-oriented extended finite element code. European Journal of Computational Mechanics 2007; 16:237-258.
21. Babuška I, Rheinbold WC. Error estimates for adaptive finite element computations. SIAM Journal on Numerical Analysis 1978; 15(4):736-754.
22. Ainsworth M, Craig AW. A posteriori error estimators in the finite element method. Numerische Mathematik 1992; 60:429-463.
23. Ainsworth M, Oden T. A unified approach to a posteriori error estimation using element residual methods. Numerische Mathematik 1993; 65(1):23-50.
24. Zienkiewicz OC, Zhu JZ. A simple error estimator and adaptive procedure for practical engineering analysis. International Journal for Numerical Methods in Engineering 1987; 24:337-357.
25. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates. Part 1: the recovery technique. International Journal for Numerical Methods in Engineering 1992; 33(7):1331-1364.
26. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates. Part 2: error estimates and adaptivity. International Journal for Numerical Methods in Engineering 1992; 33(7): 1365-1382.
27. Ainsworth M, Oden JT. A Posteriori Error Estimation in Finite Element Analysis. Wiley: New York, 2000. ISBN: 0-471-29411-X.
28. Ainsworth M, Oden JT. A posteriori error estimation in finite element analysis. Computer Methods in Applied Mechanics and Engineering 1997; 142:1-88.
29. Barros FB, Proenca SPB, de Barcellos CS. Generalized finite element method in structural nonlinear analysis - a p adaptive strategy. Computational Mechanics 2004; 33:95-107.
30. Barros FB, Proenca SPB, de Barcellos CS. On error estimator and p-adaptivity in the generalized finite element method. International Journal for Numerical Methods in Engineering 2004; 60:2373-2398.
31. Strouboulis T, Zhang L, Wang D, Babuška I. A posteriori error estimation for generalized finite element methods. Computer Methods in Applied Mechanics and Engineering 2006; 195(9-12):852-879.
32. Xiao QZ, Karihaloo BL. Improving the accuracy of xfem crack tip fields using higher order quadrature and statically admissible stress recovery. International Journal for Numerical Methods in Engineering 2006; 66: 1378-1410.
33. Barlow J. Optimal stress locations in finite element models. International Journal for Numerical Methods in Engineering 1976; 10:(2)243-251.
34. Bordas S, Duflot M, Le P. A simple error estimator for extended finite elements. Communications in Numerical Methods in Engineering 2008; DOI: 10.1002/cnm.1001.
35. Bordas S, Duflot M. Derivative recovery and a posteriori error estimate for extended finite elements. Computer Methods in Applied Mechanics and Engineering 2007; 196:3381-3399.
36. Tabbara M, Blacker T, Belytschko T. Finite element derivative recovery by moving least square interpolants. Computer Methods in Applied Mechanics and Engineering 1994; 117:211-223.
37. Oden JT, Brauchli HJ. On the calculation of consistent stress distributions in finite element approximations. International Journal for Numerical Methods in Engineering 1971; 3:317-325.
38. Hinton E, Campbell JS. Local and global smoothing of discontinuous finite element functions using a least squares method. International Journal for Numerical Methods in Engineering 1974; 8:461-480.
39. Laborde P, Pommier J, Renard Y, Salaun M. High order extended finite element method for cracked domains. International Journal for Numerical Methods in Engineering 2004; 190(47):6183-6200.
40. Béchet E, Minnebo H, Moës N, Burgardt B. Improved implementation and robustness study of the X-FEM for stress analysis around cracks. International Journal for Numerical Methods in Engineering 2005; 64:1033-1056.
41. Menouillard T, Réthoré J, Combescure A, Bung H. Efficient explicit time stepping for the extended finite element method (X-FEM). International Journal for Numerical Methods in Engineering 2006; 68:911-939.
42. Chessa J, Wang H, Belytschko T. On the construction of blending elements for local partition of unity enriched finite elements. International Journal for Numerical Methods in Engineering 2003; 57:1015-1038.
43. Gracie R, Belytschko T. An assumed strain blending element formulation for linear elastic fracture mechanics. World Congress in Computational Mechanics VII, Los Angeles, U.S.A., 2006.