Fictitious domain method with boundary value correction using penalty-free Nitsche method
Fictitious domain method with boundary value correction using penalty-free Nitsche method
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DOI：
10.1515/jnma-2016-1103
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发表时间：
2016-10
影响因子：
3
通讯作者：
Thomas Boiveau;E. Burman;S. Claus;M. Larson
中科院分区：
文献类型：
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作者：
Thomas Boiveau;E. Burman;S. Claus;M. Larson
本文考虑了一种基于Nitsche类型方法的无惩罚虚拟域方法。为了允许使用几何的分段仿射近似的高阶近似，我们使用基于泰勒展开的从近似到物理边界的边界值校正技术。为了保证该方法的稳定性，在边界区考虑了鬼罚稳定。我们证明了在h1 -范数下的最优误差估计和在l2 -范数下的次优估计。次优性是由于我们的公式缺乏伴随一致性。数值结果证实了理论研究的正确性。
Abstract In this paper, we consider a fictitious domain approach based on a Nitsche type method without penalty. To allow for high order approximation using piecewise affine approximation of the geometry we use a boundary value correction technique based on Taylor expansion from the approximate to the physical boundary. To ensure stability of the method a ghost penalty stabilization is considered in the boundary zone. We prove optimal error estimates in the H1-norm and estimates suboptimal by 𝓞(h1/2) in the L2-norm. The suboptimality is due to the lack of adjoint consistency of our formulation. Numerical results are provided to corroborate the theoretical study.