Adaptive refinement for a local error bound based on duality
Abstract
This paper presents the basis of an adaptive mesh refinement technique aimed at reducing a local error, i.e. the error in a local quantity, which is defined as the integral of a stress or a displacement in a given subregion. Two pairs of dual solutions, one corresponding to the applied load and the other to the virtual action, dual of the local quantity, are used to bound the local error and to provide the element error indicators for the adaptive process. A test case is used to exemplify the behaviour of the technique.
References
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[2] J .P.M. Almeida, J.A.T. Freitas. Alternative approach to the formulation of hybrid equilibrium finite elements. Computers & Structures, 40(4) : 1043- 1047, 1991.
[3] J .P.M. Almeida, J .A.T. Freitas. Continuity conditions for finite element analysis of solids. Int. J. Num. Meth. Eng., 33: 845- 853, 1992.
[4] I. Babuska, A. Miller. The post-processing approach in the finite element method (parts 1, 2 and 3). Int. J. Num. Meth. Eng. , 20: 1085- 1129, 2311-2324, 1984.
[5] I. Babuska, W.C. Rheinbolt. A posteriori error estimates for the finite element method. Int. J. Num. Meth. Eng, 12: 1597- 1615, 1978.
Published
2023-01-26
Issue
pp. 565-574
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Almeida Pereira, O. J. B., & Moitinho de Almeida, J. P. (2023). Adaptive refinement for a local error bound based on duality. Computer Assisted Methods in Engineering and Science, 10(4), 565-574. https://cames3.ippt.pan.pl/index.php/cames/article/view/1065
