Practical methods for a posteriori error estimation in engineering applications

International Journal for Numerical Methods in Engineering

Volumn 56, Issue 8, 2003, Pages 1193-1224

  Prudhomme, Serge ^a   Oden, J Tinsley ^a   Westermann, Tim ^b   Bass, Jon ^b   Botkin, Mark E ^c  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b ALTAIR ENGINEERING   (United States)

^c GENERAL MOTORS CORPORATION   (United States)

Author keywords

Dual problem; Goal oriented error estimation; Linear elasticity; Quantity of interest; Upper and lower bounds

Indexed keywords

COMPUTATIONAL METHODS; ERROR ANALYSIS; LINEAR EQUATIONS;

POSTERIORI ERROR ESTIMATION;

NUMERICAL METHODS;

MODELING ERROR;

EID: 0037469618     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.609     Document Type: Article

References (23)

1. Ainsworth M, Oden JT. A Posteriori Error Estimation in Finite Element Analysis. Wiley: New York, 2000.
2. Ladevèze P, Leguillon D. Error estimate procedure in the finite element method and applications. SIAM Journal of Numerical Analysis 1983; 20:485-509.
3. Babuşka I, Miller A. The post-processing approach in the finite element method-Part 3: A-posteriori error estimates and adaptive mesh selection. International Journal for Numerical Methods in Engineering 1984; 20:23 11-2324.
4. Bank RE, Weiser A. Some a posteriori error estimators for elliptic partial differential equations. Mathematics of Computation 1985; 44(170):283-301.
5. Bank RE. Hierarchical bases and the finite element method. Acta Numerica 1996; 5:1-43.
6. Ainsworth M, Oden JT, A posteriori error estimation in finite element analysis. Computer Methods in Applied Mechanics and Engineering 1997; 142(1-2):1-88.
7. Verfürth R. A Review of A Posteriori Error Estimation and Adaptive Mesh-refinement Techniques. Wiley-Teubner: Stuttgart, 1996.
8. Becker R, Rannacher R. A feedback approach to error control in finite elements methods: Basic analysis and examples. East-West Journal of Numerical Mathematics 1996; 4:237-264.
9. Rannacher R, Stuttmeier FT. A posteriori error control in finite element methods via duality techniques: Application to perfect plasticity. Computational Mechanics 1998; 21:123-133.
10. Oden JT, Prudhomme S. A technique for a posteriori error estimation of h-p approximations of the Stokes equations. In Advances in Adaptive Computational Methods in Mechanics. Ladevèze P, Oden JT (eds). Elsevier: Amsterdam, 1998; 43-63.
11. Ainsworth M, Kelly DW, Sloan IH, Wang SL. Post-processing with computable error bounds for the finite element approximation of a nonlinear heat conduction problem. IMA Journal of Numerical Analysis 1997; 17:547-561.
12. Paraschivoiu M, Patera AT. A hierarchical duality approach to bounds for the outputs of partial differential equations. Computer Methods in Applied Mechanics and Engineering 1998; 158:389-407.
13. Peraire J, Patera AT. Bounds for linear-functional outputs of coercive partial differential equations: local indicators and adaptive refinement. In Advances in Adaptive Computational Methods in Mechanics, Ladevèze P, Oden JT (eds). Elsevier: Amsterdam, 1998; 199-215.
14. Prudhomme S, Oden JT. On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors. Computer Methods in Applied Mechanics and Engineering 1999; 176:313-331.
15. Oden JT, Prudhomme S. Goal-oriented error estimation and adaptivity for the finite element method. Computers and Mathematics with Applications 2001; 41(5-6):735-756.
16. Szabó B, Babuŝka I. Finite Analysis. Wiley, 1991.
17. Oden JT, Optimal h-p finite element methods. Computer Methods in Applied Mechanics and Engineering 1994; 112:309-331.
18. Babuška I, Rheinboldt W. On the reliability and optimality of the finite element method. Computers and Structures 1979; 10:87-94.
19. Oden JT, Demkowicz L, Westermann T, Rachowicz W. Toward a universal h-p adaptive finite element strategy. Part 2. A posteriori error estimates. Computer Methods in Applied Mechanics and Engineering 1989; 77: 79-120.
20. Huerta A, Diez P, Rodriguez-Ferran A, Pijaudier-Cabot G. Error estimation and adaptive finite element analysis of softening solids. In Advances in Adaptive Computational Methods in Mechanics, Ladevèze P, Oden JT (eds). Elsevier: Amsterdam, 1998; 333-347.
21. Babuška I, Strouboulis T, Gangaraj SK. Guaranteed computable bounds for the exact error in the finite element solution Part I: One-dimensional model problem. Computer Methods in Applied Mechanics and Engineering 1999; 176:51-79.
22. Strouboulis T, Babuška I, Gangaraj SK. Guaranteed computable bounds for the exact error in the finite element solution-Part II: bounds for the energy norm of the error in two dimensions. International Journal for Numerical Methods in Engineering 2000: 47:427-475.
23. Giles M, Süli E. An introduction to a posteriori error analysis and adjoints. In Nato RTO/NASA/VKI Lecture Series, NASA Ames Research Center, CA (10-14 Sept.) and The von Karman Institute for Fluid Dynamics, Rhode-Saint-Genèse, Belgium (15-19 Oct.), 2001.