Patch recovery based on complementary energy

International Journal for Numerical Methods in Engineering

Volumn 59, Issue 11, 2004, Pages 1501-1538

  Ubertini, F ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Compatibility; Complementary energy; Error estimation; Finite element; Patch; Recovery

Indexed keywords

CHEMICAL ELEMENTS; COST EFFECTIVENESS; NUMERICAL ANALYSIS; STRESSES;

COMPLEMENTARY ENERGY; EQUILIBRATED STRESS FIELD; PATCH RECOVERY;

NUMERICAL METHODS;

FINITE ELEMENT METHOD; STRESS ANALYSIS;

EID: 1842843067     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.924     Document Type: Article

References (32)

1. Ainsworth M, Oden JT. A Posteriori Error Estimation in Finite Element Analysis. Wiley: New York, 2000.
2. Lo SH, Lee CK. On using different recovery procedures for the construction of smoothed stress in finite element method. International Journal for Numerical Methods in Engineering 1998; 43:1223-1252.
3. Tessler A, Riggs HR, Freese CE, Cook GM. An improved variational method for finite element stress recovery and a posteriori error estimation. Computer Methods in Applied Mechanics and Engineering 1998; 155:15-30.
4. Yazdani AA, Riggs HR, Tessler A. Stress recovery and error estimation for shell structures. International Journal for Numerical Methods in Engineering 2000; 47:1825-1840.
5. de Miranda S, Ubertini F. Recovery of consistent stresses for compatible finite elements. Computer Methods in Applied Mechanics and Engineering 2002; 191:1595-1609.
6. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates. Part I: the recovery technique. International Journal for Numerical Methods in Engineering 1992; 33:1331-1364.
7. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates. Part II: error estimates and adaptivity. International Journal for Numerical Methods in Engineering 1992; 33:1365-1382.
8. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery (SPR) and adaptive finite element refinement. Computer Methods in Applied Mechanics and Engineering 1992; 101:207-224.
9. Wiberg N, Abdulwahab F. Patch recovery based on superconvergent derivatives and equilibrium. International Journal for Numerical Methods in Engineering 1993; 36:2703 2724.
10. Blacker T, Belytschko T. Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. International Journal for Numerical Methods in Engineering 1994; 37:517-536.
11. Wiberg N, Abdulwahab F, Ziukas S. Enhanced superronvergent patch recovery incorporating equilibrium and boundary conditions. International Journal for Numerical Methods in Engineering 1994; 37:3417-3440.
12. Wiberg N, Abdulwahab F, Li XD. Error estimation and adaptive procedures based on superconvergent patch recovery (SPR) techniques. Archives of Computational Methods in Engineering 1997; 4(3):203-242.
13. Lee T, Park HC, Lee SW. A superconvergent stress recovery technique with equilibrium constraint. International Journal for Numerical Methods in Engineering 1997; 40:1139-1160.
14. Kvamsdal T, Okstad KM. Error estimation based on superconvergent patch recovery using statically admissible stress fields. International Journal for Numerical Methods in Engineering 1998; 42:443-472.
15. Park HC, Shin S-H. Element stress recovery technique with equilibrium constraints for superconvergence boundary stress extraction. AIAA Journal 1999; 37:623-628.
16. Okstad KM, Kvamsdal T, Mathisen KM. Superconvergent patch recovery for plate problems using statically admissible stress resultant fields. International Journal for Numerical Methods in Engineering 1999; 44:697-727.
17. Boroomand B, Zienkiewicz OC. Recovery by equilibrium in patches (REP). International Journal for Numerical Methods in Engineering 1997; 40:137-164.
18. Boroomand B, Zienkiewicz OC. An improved REP recovery and the effectivity robustness test. International Journal for Numerical Methods in Engineering 1997; 40:3247-3277.
19. Zienkiewicz OC, Boroomand B, Zhu JZ. Recovery procedures in error estimation and adaptivity. Part I: adaptivity in linear problems. Computer Methods in Applied Mechanics and Engineering 1999; 176:111-125.
20. Ubertini F. Stress recovery by compatibility in patches. In Proceedings of the Fifth World Congress on Computational Mechanics, Mang HA, Rammerstorfer FG, Eberhardsteiner J (eds), 7-12 July 2002, Vienna, Austria.
21. Fraeijs de Veubeke B. Displacement and equilibrium models in the finite element method. In Stress Analysis, Zienkiewicz OC, Holister GS (eds). Wiley: London, 1965.
22. Ladevèze P, Leguillon D. Error estimate procedure in the finite element method and applications. SIAM Journal on Numerical Analysis 1983; 20:485-509.
23. Stein E, Ahmad R. An equilibrium method for stress calculation using finite element displacement models. Computer Methods in Applied Mechanics and Engineering 1977; 10:175-198.
24. Kelly DW. The self-equilibration of residuals and complementary a posteriori error estimates in the finite element method. International Journal for Numerical Methods in Engineering 1984; 20:1491-1506.
25. Ohnimus S, Stein E, Walhorn E. Local error estimates of FEM for displacements and stresses in linear elasticity by solving local Neumann problems. International Journal for Numerical Methods in Engineering 2001; 52:727-746.
26. Allman DJ. A quadrilateral finite element including vertex rotations for plane elasticity analysis. International Journal for Numerical Methods in Engineering 1988; 26:717-730.
27. Babuška I, Strouboulis T, Upadhyay CS. A model study of the quality of a posteriori error estimators for linear elliptic problems. Error estimation in the interior of patchwise uniform grids of triangles. Computer Methods in Applied Mechanics and Engineering 1994; 114:307-378.
28. Babuška I, Strouboulis T, Upadhyay CS, Gangaraj SK, Copps K. Validation of a posteriori error estimators by numerical approach. International Journal for Numerical Methods in Engineering 1994; 37:1073-1123.
29. Babuška I, Strouboulis T, Upadhyay CS. A model study of a posteriori error estimators for finite element solution of linear elliptic problems, with particular reference to the behavior near the boundary. International Journal for Numerical Methods in Engineering 1997; 40:2521-2577.
30. Zienkiewicz OC, Taylor RL. The Finite Element Method (4th edn). vol. I. McGraw-Hill: New York, 1989.
31. Pian THH. Hybrid models. In Numerical and Computer Methods in Structural Mechanics, Fenves SJ. Perrone R, Robinson R, Schonbrich WC (eds). Academic Press: New York, 1973; 50-80.
32. Zienkiewicz OC, Zhu JZ. Superconvergence and the superconvergent patch recovery. Finite Elements in Analysis and Design 1995; 19:11-23.