Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis
Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis
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DOI：
10.1007/s00211-019-01079-x
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发表时间：
2018-06
影响因子：
2.1
通讯作者：
A. Buffa;Jürgen Dölz;S. Kurz;S. Schöps;Rafael Vázquez Hernández;Felix Wolf
中科院分区：
文献类型：
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作者：
A. Buffa;Jürgen Dölz;S. Kurz;S. Schöps;Rafael Vázquez Hernández;Felix Wolf
我们定义了多斑几何上de Rham复合体的一致b样条离散化。我们介绍并分析了这些空间上插值算子的性质，这些插值算子与曲面微分算子交换。在这些结果的基础上，我们得到了在各自能量空间下最优阶的新的收敛结果，并提供了轨迹空间的样条离散的近似性质，以便应用于等几何边界元方法理论。我们的分析可以直接推广到有限元方法。
We define a conforming B-spline discretisation of the de Rham complex on multipatch geometries. We introduce and analyse the properties of interpolation operators onto these spaces which commute w.r.t. the surface differential operators. Using these results as a basis, we derive new convergence results of optimal order w.r.t. the respective energy spaces and provide approximation properties of the spline discretisations of trace spaces for application in the theory of isogeometric boundary element methods. Our analysis allows for a straight forward generalisation to finite element methods.