Estimation of modeling error in computational mechanics

Journal of Computational Physics

Volumn 182, Issue 2, 2002, Pages 496-515

  Oden, J Tinsley ^a   Prudhomme, Serge ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

A posteriori modeling error estimation; Goal oriented methods; Hierarchical modeling; Nonlinear continuum mechanics

Indexed keywords

COMPUTATION THEORY; COMPUTATIONAL MECHANICS; CONTINUUM MECHANICS; ERRORS;

A POSTERIORI MODELING ERROR ESTIMATION; FINE MODELS; GOAL-ORIENTED; GOAL-ORIENTED METHOD; HIERARCHICAL MODEL; MODEL ERROR ESTIMATION; MODEL ERRORS; NONLINEAR CONTINUUM MECHANICS; POSTERIORI; QUANTITY OF INTEREST;

FLUID MECHANICS;

EID: 0036865855     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2002.7183     Document Type: Article

References (19)

1. M. Ainsworth, A posteriori error estimation for fully discrete hierarchic models of elliptic boundary value problems on thin domains, Numer. Math. 80, 325 (1998).
2. M. Ainsworth and J. T. Oden, A Posteriori Error Estimation in Finite Element Analysis (Wiley, New York, 2000).
3. I. Babuška and T. Strouboulis, The Finite Element Method and Its Reliability (Oxford Univ. Press, Oxford, 2001).
4. R. Becker and R. Rannacher, A feedback approach to error control in finite elements methods: Basic analysis and examples, East-West J. Numer. Math. 4, 237 (1996).
5. R. Becker and R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods, Acta Numer., Vol. 10, pp. 1-102, edited by A. Iserles, Ed., (Cambridge Univ. Press, 2002).
6. J. R. Cho and I T. Oden, Local a posteriori error estimates of hierarchical models for plate- and shell-like structures, Comput. Methods Appl. Mech. Eng. 149, 33 (1997).
7. P. Houston and E. Süli, hp-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems, SIAM J. Sci. Comput. 23, 1226 (2001).
8. M. G. Larson and T. J. Barth, A posteriori error estimation for adaptive discontinuous Galerkin approximations of hyperbolic systems, Lect. Notes Comput. Sci. Eng. 11, 363 (2000).
9. Y. Maday, A. Patera, and J. Peraire, A general formulation for a posteriori bounds for output functionals of partial differential equations; application to the eigenvalue problem, C. R. Acad. Sci. Sér 328, 823 (1999).
10. J. T. Oden, Adaptive modeling in solid mechanics, in Proc. Second European Congress on Computational Mechanics, Vol. 6, edited by Z. Waszczyszyn, and J. Pamin, Eds., (Vesalius Publishers, Cracow, 2001).
11. J. T. Oden and S. Prudhomme, Goal-oriented error estimation and adaptivity for the finite element method, Comput. Math. Appl. 41, 735 (2001).
12. J. T. Oden, S. Prudhomme, D. Hammerand, and M. Kuczma, Modeling error and adaptivity in nonlinear continuum mechanics, Comput. Methods Appl. Mech. Eng. 190, 6663 (2001).
13. J. T. Oden and K. Vemaganti, Estimation of local modeling error and goal-oriented modeling of heterogeneous materials; Part I: Error estimates and adaptive algorithms, J. Comput. Phys. 164, 22 (2000).
14. J. T. Oden and T. I. Zohdi, Analysis and adaptive modeling of highly heterogeneous elastic structures, Comput. Methods Appl. Mech. Eng. 148, 367 (1997).
15. 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. Eng. 150, 289 (1997).
16. S. Prudhomme and J. T. Oden, On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors, Comput. Methods Appl. Mech. Eng. 176, 313 (1999).
17. R. Rannacher, Adaptive Galerkin finite element methods for partial differential equations, J. Comput. Appl. Math. 128, 205 (2001).
18. K. Vemaganti and J. T. Oden, Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. II. A computational environment for adaptive modeling of heterogeneous elastic solids, Comput. Methods Appl. Mech. Eng. 190, 6089 (2001).
19. T. I. Zohdi, J. T. Oden, and G. J. Rodin, Hierarchical modeling of heterogeneous bodies, Comput. Methods Appl. Mech. Eng. 138, 273 (1996).