On some new recovery-based a posteriori error estimators

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 37-40, 2006, Pages 4794-4815

  Maisano, G ^a   Micheletti, S ^a   Perotto, S ^a   Bottasso, C L ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

A posteriori analysis; Error estimators; Finite elements; Recovery techniques

Indexed keywords

COMPUTER SIMULATION; ERROR ANALYSIS; FINITE ELEMENT METHOD; GRADIENT METHODS; QUADRATIC PROGRAMMING;

A POSTERIORI ANALYSIS; ERROR ESTIMATORS; RECOVERY TECHNIQUES;

ESTIMATION;

COMPUTER SIMULATION; ERROR ANALYSIS; ESTIMATION; FINITE ELEMENT METHOD; GRADIENT METHODS; QUADRATIC PROGRAMMING;

EID: 33744906082     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.07.024     Document Type: Article

References (30)

1. Ainsworth M., and Oden J.T. A Posteriori Error Estimation in Finite Element Analysis (2000), Wiley, New York
2. Bottasso C.L., and Shephard M.S. Parallel adaptive finite element Euler flow solver for rotary wing aerodynamics. AIAA J. 35 (1997) 937-944
3. Bruch J.C. Free surface seepage problems solved using: (a) the Zienkiewicz-Zhu error estimation procedure; and (b) a parallel computer. Pitman Res. Notes Math. Ser. 282 (1993) 98-104
4. Carstensen C. All first-order averaging techniques for a posteriori finite element error control on unstructured grids are efficient and reliable. Math. Comp. 73 (2004) 1153-1165
5. Carstensen C. Some remarks on the history and future of averaging techniques in a posteriori finite element error analysis. ZAMM Z. Angew. Math. Mech. 84 (2004) 3-21
6. Carstensen C., and Bartels S. Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. I: Low order conforming, nonconforming, and mixed FEM. Math. Comp. 71 (2001) 945-969
7. Ciarlet P. The Finite Element Method for Elliptic Problems (1978), North-Holland, Amsterdam
8. Duran R., Muschietti M.A., and Rodri{dotless}́guez R. On the asymptotic exactness of error estimators for linear triangular finite elements. Numer. Math. 59 (1991) 107-127
9. Isaacson E., and Keller H. Analysis of Numerical Methods (1966), Wiley, New York
10. Kri{dotless}́zek M., and Neittaanmäki P. Superconvergence phenomenon in the finite element method arising from averaging gradients. Numer. Math. 45 (1984) 105-116
11. Kri{dotless}́zek M., and Neittaanmäki P. On a global superconvergence of the gradient of linear triangular elements. J. Comput. Appl. Math. 18 (1987) 221-233
12. Lakhany A.M., Marek I., and Whiteman J.R. Superconvergence results on mildly structured triangulations. Comput. Methods Appl. Mech. Engrg. 189 (2000) 1-75
13. Lawrence K.L., and Nambiar R.V. The Zienkiewicz-Zhu error estimator for multiple material problems. Commun. Appl. Numer. Methods 8 (1992) 273-277
14. 2 norms. Comp. Struct. 53 (1994) 907-919
15. G. Maisano, A posteriori error estimator methods based on recovery techniques, Degree Thesis, Politecnico di Milano, 2004 (in Italian).
16. D.J. Mavriplis, Revisiting the least-square procedure for gradient reconstruction on unstructured meshes, NASA/CR Report, 2003-06, 2003.
17. Micheletti S., and Perotto S. Reliability and efficiency of an anisotropic Zienkiewicz-Zhu error estimator. Comput. Methods Appl. Mech. Engrg. 195 (2006) 799-835
18. Naga A., and Zhang Z. A posteriori error estimates based on the polynomial preserving recovery. SIAM J. Numer. Anal. 42 (2004) 1780-1800
19. Pawlak T.P., Wheeler M.J., and Yunus S.M. Application of the Zienkiewicz-Zhu error estimator for plate and shell analysis. Int. J. Numer. Methods Engrg. 29 (1990) 1281-1298
20. Picasso M. Numerical study of the effectivity index for an anisotropic error indicator based on Zienkiewicz-Zhu error estimator. Comm. Numer. Methods. Engrg. 19 (2003) 13-23
21. Rodríguez R. Some remarks on Zienkiewicz-Zhu estimator. Numer. Methods Part. Diff. Eq. 10 (1994) 625-635
22. Shmitt V., and Charpin F. Pressure distribution on the ONERA M6 wing at transonic Mach number. AGARD R-702 B1 (1982) 1-44
23. Verfürth R. A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques (1996), Wiley-Teubner, New York
24. Xu J., and Zhang Z. Analysis of recovery type a posteriori error estimators for mildly structured grids. Math. Comput. 73 (2004) 1139-1152
25. Yan N., and Zhou A. Gradient recovery type a posteriori error estimation for finite element approximations on irregular meshes. Comput. Methods Appl. Mech. Engrg. 190 (2001) 4289-4299
26. Zhang Z., and Zhu J.Z. Superconvergence of the derivative patch recovery technique and a posteriori error estimation. In: Babuska I., Flaherty J.E., Henshaw W.D., Hopcroft J.E., Oliger J.E., and Tezduyar T. (Eds). Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations. IMA Volumes in Mathematics and its Applications vol. 75 (1995), Springer, New York 431-450
27. Zienkiewicz O.C., and Zhu J.Z. A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Numer. Methods Engrg. 24 (1987) 337-357
28. Zienkiewicz O.C., and Zhu J.Z. The superconvergent patch recovery (SPR) and adaptive finite element refinement. Comput. Methods Appl. Mech. Engrg. 101 (1992) 207-224
29. Zienkiewicz O.C., and Zhu J.Z. The superconvergent patch recovery and a posteriori error estimates. I: The recovery technique. Int. J. Numer. Methods Engrg. 33 (1992) 1331-1364
30. Zienkiewicz O.C., and Zhu J.Z. The superconvergent patch recovery and a posteriori error estimates. II: Error estimates and adaptivity. Int. J. Numer. Methods Engrg. 33 (1992) 1365-1382