×

Practical methods for a posteriori error estimation in engineering applications. (English) Zbl 1038.74045

Summary: This work presents an extension of the goal-oriented error estimation technique to the engineering analysis of three-dimensional linear elastic bodies. In the series of examples shown, the errors are estimated with respect to local displacement and stress components. The paper also introduces novel means to compute lower bounds on the error in energy norm based on a cost-effective postprocessing of upper bound error estimates. The numerical results indicate that the method can be used effectively for complex engineering applications.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
65N15 Error bounds for boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] A Posteriori Error Estimation in Finite Element Analysis. Wiley: New York, 2000.
[2] Ladevèze, SIAM Journal on Numerical Analysis 20 pp 485– (1983)
[3] Babu?ka, International Journal for Numerical Methods in Engineering 20 pp 2311– (1984)
[4] Bank, Mathematics of Computation 44 pp 283– (1985)
[5] Bank, Acta Numerica 5 pp 1– (1996)
[6] Ainsworth, Computer Methods in Applied Mechanics and Engineering 142 pp 1– (1997)
[7] A Review of A Posteriori Error Estimation and Adaptive Mesh-refinement Techniques. Wiley-Teubner: Stuttgart, 1996. · Zbl 0853.65108
[8] Becker, East-West Journal of Numerical Mathematics 4 pp 237– (1996)
[9] Rannacher, Computational Mechanics 21 pp 123– (1998)
[10] A technique for a posteriori error estimation of h-p approximations of the Stokes equations. In Advances in Adaptive Computational Methods in Mechanics, (eds). Elsevier: Amsterdam, 1998; 43-63.
[11] Ainsworth, IMA Journal of Numerical Analysis 17 pp 547– (1997)
[12] Paraschivoiu, Computer Methods in Applied Mechanics and Engineering 158 pp 389– (1998)
[13] Bounds for linear-functional outputs of coercive partial differential equations: local indicators and adaptive refinement. In Advances in Adaptive Computational Methods in Mechanics, (eds). Elsevier: Amsterdam, 1998; 199-215.
[14] Prudhomme, Computer Methods in Applied Mechanics and Engineering 176 pp 313– (1999)
[15] Oden, Computers and Mathematics with Applications 41 pp 735– (2001)
[16] Finite Element Analysis. Wiley, 1991.
[17] Oden, Computer Methods in Applied Mechanics and Engineering 112 pp 309– (1994)
[18] Babu?ka, Computers and Structures 10 pp 87– (1979)
[19] Oden, Computer Methods in Applied Mechanics and Engineering 77 pp 79– (1989)
[20] Error estimation and adaptive finite element analysis of softening solids. In Advances in Adaptive Computational Methods in Mechanics, (eds). Elsevier: Amsterdam, 1998; 333-347.
[21] Babu?ka, Computer Methods in Applied Mechanics and Engineering 176 pp 51– (1999)
[22] Strouboulis, International Journal for Numerical Methods in Engineering 47 pp 427– (2000)
[23] An introduction to a posteriori error analysis and adjoints. In Nato RTO/NASA/VKI Lecture Series, NASA Ames Research Center, CA (10-14Sept.) and The von Karman Institute for Fluid Dynamics, Rhode-Saint-Genèse, Belgium (15-19Oct.), 2001.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.