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An improved local error estimate in adaptive finite element analysis based on element energy projection technique

Haohan Sun (Department of Civil Engineering, Tsinghua University, Beijing, China)
Si Yuan (Tsinghua University, Beijing, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 3 February 2023

Issue publication date: 14 February 2023




An improved adaptive finite element analysis based on local error estimate is proposed via the element energy projection (EEP) technique. This paper aims to discuss the aforementioned idea.


The computational region for a posteriori error estimation based on EEP method is further confined to a critical set of local elements generated in the previous adaptive step, enhancing efficiency while maintaining accuracy. The adaptive procedure incorporated with hierarchical mesh refinement is then developed.


The effectiveness of the improved error estimation of the overall adaptive analysis is confirmed by several benchmark examples. The results show that the shrinkage of the local computational region has little negative influence on the accuracy of a posteriori error estimation, thus yielding an improved adaptive procedure with simplified logic and reduced cost.


By localizing the computational region for error estimation, two crucial but cumbersome tricks, i.e. treatments of virtual elements and hanging nodes, are removed, giving the proposed approach full clarity and flexibility. The improved adaptive procedure characterizes simpler and faster computational algorithm and can produce results with required accuracy measured in maximum norm.



The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (grant nos. 51878383, 51378293).


Sun, H. and Yuan, S. (2023), "An improved local error estimate in adaptive finite element analysis based on element energy projection technique", Engineering Computations, Vol. 40 No. 1, pp. 246-264.



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