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New analytical tools for HDG in elasticity, with applications to elastodynamics


Authors: Shukai Du and Francisco-Javier Sayas
Journal: Math. Comp. 89 (2020), 1745-1782
MSC (2010): Primary 65N30, 65M60, 74B05
DOI: https://doi.org/10.1090/mcom/3499
Published electronically: December 30, 2019
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Abstract: We present some new analytical tools for the error analysis of hybridizable discontinuous Galerkin (HDG) methods for linear elasticity. These tools allow us to analyze more variants of the HDG method using the projection-based approach, which renders the error analysis simple and concise. The key result is a tailored projection for the Lehrenfeld-Schöberl type HDG (HDG+ for simplicity) methods. By using the projection we recover the error estimates of HDG+ for steady-state and time-harmonic elasticity in a simpler analysis. We also present a semidiscrete (in space) HDG+ method for transient elastic waves and prove it is uniformly-in-time optimal convergent by using the projection-based error analysis. Numerical experiments supporting our analysis are presented at the end.


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Additional Information

Shukai Du
Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
Address at time of publication: 1324 Gibbs Ave, Falcon Heights, Minnesota, 55108
Email: shukaidu@udel.edu

Francisco-Javier Sayas
Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716

DOI: https://doi.org/10.1090/mcom/3499
Keywords: Discontinuous Galerkin method, hybridization, optimal convergence, elastic waves
Received by editor(s): March 27, 2019
Received by editor(s) in revised form: August 23, 2019, and September 13, 2019
Published electronically: December 30, 2019
Additional Notes: This work was partially supported by the NSF grant DMS-1818867.
Article copyright: © Copyright 2019 American Mathematical Society