Robust error estimation for lowest-order approximation of nearly incompressible elasticity
Robust error estimation for lowest-order approximation of nearly incompressible elasticity
复制标题
近不可压缩弹性最低阶近似的鲁棒误差估计
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
D. Silvester
中科院分区：
文献类型：
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作者：
Arbaz Khan;C. Powell;D. Silvester
我们考虑经典线弹性力学的所谓Herrmann和流体静力学混合公式，并分析了局部稳定化的$P_1-P_0元有限元近似的误差。首先，我们证明了离散问题的稳定性估计，并建立了相关能量误差的先验估计。其次，我们考虑了基于残差的后验误差估计和局部Poisson问题估计。我们建立了与LAM‘{e}系数无关的能量误差的界，并证明了估计器在不可压缩极限下是稳健的。需要解决的一个关键问题是压力稳定的要求。数值结果验证了理论的正确性。使用的软件在网上可以买到。
We consider so-called Herrmann and Hydrostatic mixed formulations of classical linear elasticity and analyse the error associated with locally stabilised $P_1-P_0$ finite element approximation. First, we prove a stability estimate for the discrete problem and establish an a priori estimate for the associated energy error. Second, we consider a residual-based a posteriori error estimator as well as a local Poisson problem estimator. We establish bounds for the energy error that are independent of the Lam'{e} coefficients and prove that the estimators are robust in the incompressible limit. A key issue to be addressed is the requirement for pressure stabilisation. Numerical results are presented that validate the theory. The software used is available online.
用于近不可压缩弹性混合近似的鲁棒后验误差估计器
影响因子：
2.9
作者：
Khan A
通讯作者：
Khan A