A Higher Order Isoparametric Fictitious Domain Method for Level Set Domains
A Higher Order Isoparametric Fictitious Domain Method for Level Set Domains
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DOI：
10.1007/978-3-319-71431-8_3
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发表时间：
2016-12
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通讯作者：
C. Lehrenfeld
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作者：
C. Lehrenfeld
本文考虑一种新的高阶精度的虚拟域方法。为了实现狄利克雷条件，我们应用经典的Nitsche方法结合基于小平面的稳定（鬼惩罚）。这两种技术相结合的高阶等参有限元空间是基于一个特殊的网格变换。网格变换是建立在一个更高的顺序准确的水平集表示，并允许减少问题的数值积分的问题，由分段线性水平集函数描述的域。这种策略的数值积分和稳定的Nitsche制定的结果在一个准确的和强大的方法相结合。我们介绍和分析它，并给出数值例子。
We consider a new fictitious domain approach of higher order accuracy. To implement Dirichlet conditions we apply the classical Nitsche method combined with a facet-based stabilization (ghost penalty). Both techniques are combined with a higher order isoparametric finite element space which is based on a special mesh transformation. The mesh transformation is build upon a higher order accurate level set representation and allows to reduce the problem of numerical integration to problems on domains which are described by piecewise linear level set functions. The combination of this strategy for the numerical integration and the stabilized Nitsche formulation results in an accurate and robust method. We introduce and analyze it and give numerical examples.