Abstract
The paper is devoted to the use of error estimators based on gradient recovery in finite element computations, where the resulting error estimates can be used as the basis for hp-adaptive mesh refinement. Due to high complexity of adaptive numerical software we have decided to take advantage of the object-oriented paradigm of software development. We discuss our implementation of the Zienkiewicz-Zhu error estimator and of selected gradient recovery techniques (averaging and superconvergent patch recovery).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Babuška, I.: Validation of a posteriori error estimators by numerical approach. Int. J. Num. Meth. Engng. 37, 1073–1123 (1994)
Barlow, J.: Optimal stress locations in finite element models. Int. J. Num. Meth. Engng. 10, 243–251 (1976)
Zienkiewicz, O.C., Zhu, J.Z.: A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Num. Meth. Engng. 24, 337–357 (1987)
Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. Part I. The recovery technique. Int. J. Num. Meth. Engng. 33, 1331–1364 (1992)
Mackinnon, R.J., Carey, G.F.: Superconvergent derivatives: a Taylor series analysis. Int. J. Num. Meth. Engng. 28, 489–509 (1989)
Blacker, T., Belytschko, T.: Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. Int. J. Num. Meth. Engng. 37, 517–536 (1994)
Sczygiol, N., Nagórka, A.: An hp-adaptive finite element method for the solidification problem based on explicit residual error estimates. In: Proceedings of Computer Methods in Mechanics, Wisla, Poland, June 3-6, pp. 3–6 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nagórka, A., Sczygiol, N. (2004). Implementation Aspects of a Recovery-Based Error Estimator in Finite Element Analysis. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2003. Lecture Notes in Computer Science, vol 3019. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24669-5_95
Download citation
DOI: https://doi.org/10.1007/978-3-540-24669-5_95
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21946-0
Online ISBN: 978-3-540-24669-5
eBook Packages: Springer Book Archive