On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors

Computer Methods in Applied Mechanics and Engineering

Volumn 176, Issue 1-4, 1999, Pages 313-331

  Prudhomme, S ^a   Oden, J T ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; FINITE ELEMENT METHOD; PROBLEM SOLVING;

ELLIPTIC PROBLEMS; ERROR ESTIMATION;

ERROR ANALYSIS;

EID: 0032669875     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00343-0     Document Type: Article

References (21)

1. [1] M. Ainsworth and J.T. Oden, A unified approach to a posteriori error estimation using element residual methods, Numer. Math. 65 (1993) 23-50.
2. [2] M. Ainsworth and J.T. Oden, A posteriori error estimation in finite element analysis, Comput. Methods Appl. Mech. Engrg. 142 (1997) 1-88.
3. [3] I. Babuška and W. Rheinboldt, A posteriori error estimates for the finite element method, Int. J. Numer. Methods Engrg. 12 (1978) 1597-1615.
4. [4] I. Babuška, T. Strouboulis, K. Copps, S.K. Gangaraj and C.S. Upadhyay, A-posteriori error estimation for finite element and generalized finite element method, TICAM Report 98-01, The University of Texas at Austin, 1998.
5. [5] R.E. Bank, Hierarchical bases and the finite element method, Acta Numerica 5 (1996) 1-43.
6. [6] R.E. Bank and R.K. Smith, A posteriori error estimates based on hierarchical bases, SIAM J. Numer. Anal. 30 (1993) 921-935.
7. [7] R.E. Bank and A. Weiser, Some a posteriori error estimates for elliptic partial differential equations, Math. Comput. 44 (1985) 283-301.
8. [8] R. Becker and R. Rannacher, A feedback approach to error control in finite elements methods: Basic analysis and examples, preprint 96-52, Institut für Angewandte Mathematik, Universität Heidelberg, 1996, Comput Mech., to appear.
9. [9] R. Becker and R. Rannacher, Weighted a posteriori error control in FE method, in: ENUMATH-95, Paris, Sept. 1995.
10. [10] L. Demkowicz, J.T. Oden, W. Rachowicz and O. Hardy, Toward a universal h-p adaptive finite element strategy. Part 1. Constrained approximation and data structure, Comput. Methods Appl. Mech. Engrg. 77 (1989) 113-180.
11. [11] A. Huerta, P. Díez, A. Rodríguez-Ferran and G. Pijaudier-Cabot, Error estimation and adaptive finite element analysis of softening solids, in: P. Ladevèze and J.T. Oden, eds., Advances in Adaptive Computational Methods in Mechanics (Elsevier, Amsterdam, 1998) 333-347.
12. [12] P. Ladevèze and D. Leguillon, Error estimate procedure in the finite element method and applications, SIAM J. Numer. Anal. 20 (1983) 485-509.
13. [13] J.T. Oden and S. Prudhomme, A technique for a posteriori error estimation of h-p approximations of the Stokes equations, in: P. Ladevèze and J.T. Oden, eds., Advances in Adaptive Computational Methods in Mechanics (Elsevier, Amsterdam, 1998) 43-63.
14. [14] J.T. Oden and J.N. Reddy, An Introduction to the Mathematical Theory of Finite Elements (John Wiley & Sons, 1976).
15. [15] M. Paraschivoiu and A.T. Patera, A hierarchical duality approach to bounds for the outputs of partial differential equations, Comput. Methods Appl. Mech. Engrg. 158 (1998) 389-407.
16. [16] M. Paraschivoiu, J. Peraire and A.T. Patera, A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations, Comput. Methods Appl. Mech. Engrg. 150 (1997) 289-312.
17. [17] J. Peraire and A.T. Patera, Bounds for linear-functional outputs of coercive partial differential equations: local indicators and adaptive refinement, in: P. Ladevèze and J.T. Oden, eds., Advances in Adaptive Computational Methods in Mechanics (Elsevier, Amsterdam, 1998) 199-215.
18. [18] R. Rannacher and F.T. Stuttmeier, A posteriori error control in finite element methods via duality techniques: Application to perfect elasticity, Preprint 97-16, Institut für Angewandte Mathematik, Universität Heidelberg, 1997, Comput. Mech., to appear.
19. [19] R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-refinement Techniques (Wiley-Teubner, 1996).
20. [20] O.C. Zienkiewicz and J.Z. Zhu, The superconvergent patch recovery and a posteriori error estimates. Part 1 : the recovery technique, Int. J. Numer. Methods Engrg. 33 (1992) 1331-1364.
21. [21] O.C. Zienkiewicz and J.Z. Zhu, The superconvergent patch recovery and a posteriori error estimates. Part 2: error estimates and adaptivity, Int. J. Numer. Methods Engrg. 33 (1992) 1365-1382.