Analysis of the shifted boundary method for the Stokes problem
Analysis of the shifted boundary method for the Stokes problem
复制标题
斯托克斯问题的平移边界法分析
DOI：
10.1016/j.cma.2019.112609
复制
发表时间：
2020
影响因子：
7.2
通讯作者：
G. Scovazzi
中科院分区：
文献类型：
--
作者：
N. M. Atallah;C. Canuto;G. Scovazzi
对Stokes流动方程的位移边界方法的稳定性和精度进行了分析。移动边界法是一种嵌入式有限元方法，其主要特点是将边界条件的应用位置从真实边界转移到代理边界，并对边界条件的值进行适当的修改(移动)。证明了与位移边界法有关的变分形式的一个inf-sup条件，并利用Strang第二引理得到了自然SBM范数下的最优误差估计。通过将Aubin-Nitsche方法推广到嵌入、非协调、混合有限元方法，我们还得到了速度场的L误差估计。
The analysis of stability and accuracy of the shifted boundary method is developed for the Stokes flow equations. The key feature of the shifted boundary method, an embedded finite element method, is the shifting of the location where boundary conditions are applied from the true to a surrogate boundary, and an appropriate modification (shifting) of the value of the boundary conditions. An inf–sup condition is proved for the variational formulation associated to the shifted boundary method and we derive, by way of Strang’s second lemma, an optimal error estimate in the natural SBM norm. We also derive an L 2-error estimate for the velocity field, by means of an extension of the Aubin–Nitsche approach to embedded, non-consistent, mixed finite element methods.