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CivilComp Proceedings
ISSN 17593433 CCP: 75
PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and Z. Bittnar
Paper 15
Error Estimation and pAdaptivity Based on the Partition of Unity Method T. Pannachet+, P. Díez* and H. Askes+
+Faculty of Civil Engineering and Geosciences, Delft University of Technology, The Netherlands
T. Pannachet, P. Díez, H. Askes, "Error Estimation and pAdaptivity Based on the Partition of Unity Method", in B.H.V. Topping, Z. Bittnar, (Editors), "Proceedings of the Sixth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 15, 2002. doi:10.4203/ccp.75.15
Keywords: error assessment, remeshing, padaptivity, partition of unity, goaloriented error estimation.
Summary
Error estimation and adaptivity are indispensable tools to make finite element analysis
applicable to engineering practice. Upper and lower bound error estimators, based
on sound mathematical principles, are needed to assess the quality of a numerical
solution.
Furthermore, flexible and robust adaptive remeshing algorithms are needed to optimise finite element discretisations, so that prescribed accuracies can be obtained at minimal computational costs. Recently, a new methodology has been developed for the formulation of interpolation functions, namely the Partition of Unity Method (PUM) [4]. Instead of an elementoriented methodology, a nodebased strategy is taken. This makes adaptivity much more flexible, since interelement compatibility of the interpolation functions is straightforward with the PUM concept [3]. Moreover, functions other than polynomials are easily added to the interpolation space, so that analytical information for certain problems (singular behaviour in cracktip problems, harmonic functions in higherorder gradient models) can be used to enrich the shape functions efficiently. In this contribution, the PUM is applied for adaptive analysis, and is driven by a residualtype error estimation. An elementbased estimate is combined to a patchbased estimate, following the work of Díez [1]. Using Dirichlet boundary conditions, a lowerbound error estimate is obtained within a simple implementational context. Thus, the complete adaptive scheme including error assessment and remeshing is performed by the combination of the PUM and the local refinement. A related issue is the concept of the socalled goaloriented error [2], whereby not the total (global) error is the quantity of interest, but derived quantities such as the stress in a given point, or the crackopening displacement. The extension of the error estimation scheme in goaloriented error assessment is addressed. Numerical examples show the capability of the adaptive technique with the error assessment. References
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