Numerical study of the effectivity index for an anisotropic error indicator based on Zienkiewicz-Zhu error estimator

Communications in Numerical Methods in Engineering

Volumn 19, Issue 1, 2003, Pages 13-23

  Picasso, M ^a  

^a EPFL   (Switzerland)

Author keywords

A posteriori error estimates; Adaptive finite elements; Anisotropic meshes

Indexed keywords

ALGORITHMS; ERROR ANALYSIS; ESTIMATION; LAPLACE TRANSFORMS;

ERROR GRADIENTS;

ANISOTROPY;

FINITE ELEMENT ANALYSIS; MODELING ERROR;

EID: 0037280081     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/cnm.546     Document Type: Article

References (17)

1. Babuska I, Strouboulis T, Upadhyay CS. A model study of the quality of a posteriori 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(4):307 378.
2. Zienkiewicz OC, Zhu JZ. A simple error estimator and adaptive procedure for practical engineering analysis. International Journal for Numerical Methods in Engineering 1987; 24(2):337-357.
3. Ainsworth M, Zhu JZ, Craig AW, Zienkiewicz OC. Analysis of the Zienkiewicz-Zhu a posteriori error estimator in the finite element method. International Journal for Numerical Methods in Engineering 1989; 28(9): 2161-2174.
4. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates. I. The recovery technique. International Journal for Numerical Methods in Engineering 1992; 33(7):1331-1364.
5. Carey GF. Generation, adaptation, and solution strategies. In Computational Grids. Taylor & Francis: Washington, DC, 1997.
6. Habashi WG, Fortin M, Dompierre J, Vallet M-G, Bourgault Y. Anisotropic mesh adaptation: a step towards a mesh-independent and user-independent CFD. In Barriers and Challenges in Computational Fluid Dynamics: ICASE/LaRC Interdiscip. Ser. Sci. Engng 6 (Hampton, VA, 1996). Kluwer Academic Publisher, Dordrecht, 1998; 99-117.
7. Ait-Ali-Yahia D, Habashi WG, Tam A, Vallet M-G, Fortin M. A directionally adaptive methodology using an edge-based error estimate on quadrilateral grids. International Journal for Numerical Methods in Fluids 1996; 23(7):673-690.
8. 2 error estimation on anisotropic tetrahedral finite element meshes. IMA Journal of Numerical Analysis 2001; 21(2):503-523.
9. Siebert KG. An a posteriori error estimator for anisotropic refinement. Numerische Mathematik 1996; 73(3):373-398.
10. Formaggia L, Perotto S. New anisotropic a priori error estimates. Numerische Mathematik 2001; 89:641-667.
11. Formaggia L, Perotto S. Anisotropic error estimates for elliptic problems. Technical Report 18, Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, Switzerland, 2000, Numerische Mathemalik, at press.
12. Rannacher R. Adaptive Galerkin finite element methods for partial differential equations. Journal of Computational and Applied Mathematics 2001; 128(1-2):205-233. Numerical analysis 2000, Vol. VII, Partial differential equations.
13. Baranger J, El-Amri H. Estimateurs a posteriori d'erreur pour le calcul adaptatif d'écoulements quasi-newtoniens. RAIRO M2AN 1991; 25(l):31-48.
14. Babuska I, Duran R, Rodriguez R. Analysis of the efficiency of an a posteriori error estimator for linear triangular finite elements. SIAM Journal for Numerical Analysis 1992; 29(4):947-964.
15. Rodríguez R. Some remarks on Zienkiewicz-Zhu estimator. Numerical Methods for Partial Differential Equations 1994; 10(5):625-635.
16. Borouchaki H, Laug P. The b12d mesh generator: Beginner's guide, user's and programmer's manual. Technical Report RT-0194, Institut National de Recherche en Informatique et Automatique (INRIA), Rocquencourt, 78153 Le Chesnay, France, 1996.
17. Picasso M. An anisotropic error indicator based on Zienkiewicz-Zhu error estimator: application to elliptic and parabolic problems. Technical Report, Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, Switzerland, 2001, SIAM Scientific Computing, submitted.