A Stabilized Nitsche Fictitious Domain Method for the Stokes Problem
A Stabilized Nitsche Fictitious Domain Method for the Stokes Problem
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DOI：
10.1007/s10915-014-9838-9
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发表时间：
2012-06
影响因子：
2.5
通讯作者：
A. Massing;M. Larson;A. Logg;M. Rognes
中科院分区：
文献类型：
--
作者：
A. Massing;M. Larson;A. Logg;M. Rognes
提出了一种求解虚拟区域上Stokes问题的新的有限元方法。证明了离散系统的inf-sup稳定性、最优阶收敛性和条件数的一致有界性。有限元公式是基于一个稳定的Nitsche方法与鬼罚款的速度和压力，以获得稳定的存在下，小切元素。我们首次证明了Nitsche虚拟域方法对三维Stokes问题的适用性。我们进一步讨论了一个通用的，灵活的和免费提供的方法和数值例子支持的理论结果。
We present a novel finite element method for the Stokes problem on fictitious domains. We prove inf-sup stability, optimal order convergence and uniform boundedness of the condition number of the discrete system. The finite element formulation is based on a stabilized Nitsche method with ghost penalties for the velocity and pressure to obtain stability in the presence of small cut elements. We demonstrate for the first time the applicability of the Nitsche fictitious domain method to three-dimensional Stokes problems. We further discuss a general, flexible and freely available implementation of the method and present numerical examples supporting the theoretical results.