New analytical tools for HDG in elasticity, with applications to elastodynamics
New analytical tools for HDG in elasticity, with applications to elastodynamics
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DOI：
10.1090/mcom/3499
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发表时间：
2019-03
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通讯作者：
Shukai Du;F. Sayas
中科院分区：
文献类型：
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作者：
Shukai Du;F. Sayas
针对线弹性力学杂交间断伽辽金(HDG)方法的误差分析问题，提出了一些新的分析工具。这些工具允许我们使用基于投影的方法来分析HDG方法的更多变体，这使得误差分析变得简单而简洁。关键结果是为Lehrenfeld-Schoberl型HDG(HDG+为简单起见)方法量身定做的投影。利用该投影，我们在更简单的分析中恢复了稳态和时间调和弹性的HDG+的误差估计。我们还提出了一种求解瞬变弹性波的半离散(空间)HDG+方法，并通过基于投影的误差分析证明了该方法是一致时间最优收敛的。最后给出了支持我们分析的数值实验结果。
We present some new analytical tools for the error analysis of hybridizable discontinuous Galerkin (HDG) method for linear elasticity. These tools allow us to analyze more variants of 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-Schoberl 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 semi-discrete (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.