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

Du, Shukai; Sayas, Francisco-Javier

doi:10.1090/mcom/3499

New analytical tools for HDG in elasticity, with applications to elastodynamics
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by Shukai Du and Francisco-Javier Sayas HTML | PDF

Math. Comp. 89 (2020), 1745-1782 Request permission

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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