Locking-free enriched Galerkin method for linear elasticity. Yi, S., Lee, S., & Zikatanov, L. SIAM Journal on Numerical Analysis, 60(1):52-75, SIAM, 2022. abstract bibtex We propose a new locking-free enriched Galerkin method for solving the linear elasticity problem. The method is based on the discontinuous Galerkin formulation, but its approximation space is a continuous piecewise linear vector-valued function space enriched by some discontinuous piecewise linear functions. An a priori error estimate of optimal order in the energy norm is proved and shown to be independent of a Lamé parameter λ, hence the proposed method is free of volumetric locking when modeling incompressible materials. Moreover, a uniform preconditioner with respect to the mesh size is established in the operator preconditioning framework. We provide several numerical examples to confirm the accuracy and the robustness of the new method and demonstrate a good performance of the preconditioner.
@article{yi2022locking,
title={Locking-free enriched Galerkin method for linear elasticity},
author={Yi, Son-Young and Lee, Sanghyun and Zikatanov, Ludmil},
journal={SIAM Journal on Numerical Analysis},
volume={60},
number={1},
pages={52-75},
year={2022},
publisher={SIAM},
abstract = { We propose a new locking-free enriched Galerkin method for solving the linear elasticity problem. The method is based on the discontinuous Galerkin formulation, but its approximation space is a continuous piecewise linear vector-valued function space enriched by some discontinuous piecewise linear functions. An a priori error estimate of optimal order in the energy norm is proved and shown to be independent of a Lamé parameter \lambda, hence the proposed method is free of volumetric locking when modeling incompressible materials. Moreover, a uniform preconditioner with respect to the mesh size is established in the operator preconditioning framework. We provide several numerical examples to confirm the accuracy and the robustness of the new method and demonstrate a good performance of the preconditioner. }
}
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