Dr Robert Bird robert.e.bird@durham.ac.uk
PDRA in Computational Solid Mechanics
A posteriori discontinuous Galerkin error estimator for linear elasticity
Bird, R.E.; Coombs, W.M.; Giani, S.
Authors
Professor William Coombs w.m.coombs@durham.ac.uk
Professor
Dr Stefano Giani stefano.giani@durham.ac.uk
Associate Professor
Abstract
This paper presents for the first time the derivation of an hp a posteriori error estimator for the symmetric interior penalty discontinuous Galerkin finite element method for linear elastic analysis. Any combination of Neumann and Dirichlet boundary conditions are admissible in the formulation, including applying Neumann and Dirichlet on different components on the same region of the boundary. Therefore, the error estimator is applicable to a variety of physical problems. The error estimator is incorporated into an hp-adaptive finite element solver and verified against smooth and non-smooth problems with closedform analytical solutions, as well as, being demonstrated on a non-smooth problem with complex boundary conditions. The hp-adaptive finite element analyses achieve exponential rates of convergence. The performances of the hp-adaptive scheme are contrasted against uniform and adaptive h refinement. This paper provides a complete framework for adaptivity in the symmetric interior penalty discontinuous Galerkin finite element method for linear elastic analysis.
Citation
Bird, R., Coombs, W., & Giani, S. (2019). A posteriori discontinuous Galerkin error estimator for linear elasticity. Applied Mathematics and Computation, 344-345, 78-96. https://doi.org/10.1016/j.amc.2018.08.039
Journal Article Type | Article |
---|---|
Acceptance Date | Aug 19, 2018 |
Online Publication Date | Oct 24, 2018 |
Publication Date | Mar 1, 2019 |
Deposit Date | Aug 21, 2018 |
Publicly Available Date | Mar 29, 2024 |
Journal | Applied Mathematics and Computation |
Print ISSN | 0096-3003 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 344-345 |
Pages | 78-96 |
DOI | https://doi.org/10.1016/j.amc.2018.08.039 |
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Copyright Statement
© 2018 The Author(s). Published by Elsevier Inc.
This is an open access article under the CC BY license.
(http://creativecommons.org/licenses/by/4.0/)
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