Volume 55, Number 5, September-October 2021
|Page(s)||1921 - 1939|
|Published online||22 September 2021|
Quasi-optimal adaptive hybridized mixed finite element methods for linear elasticity
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
* Corresponding author; email@example.com
Accepted: 18 August 2021
For the planar Navier–Lamé equation in mixed form with symmetric stress tensors, we prove the uniform quasi-optimal convergence of an adaptive method based on the hybridized mixed finite element proposed in Gong et al. [Numer. Math. 141 (2019) 569–604]. The main ingredients in the analysis consist of a discrete a posteriori upper bound and a quasi-orthogonality result for the stress field under the mixed boundary condition. Compared with existing adaptive methods, the proposed adaptive algorithm could be directly applied to the traction boundary condition and be easily implemented.
Mathematics Subject Classification: 65N12 / 65N15 / 65N30 / 65N50
Key words: linear elasticity / mixed finite element / hybridization / convergence / quasi-optimality
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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