论文标题
Sobolev差异形式的局部有限元近似
Local Finite Element Approximation of Sobolev Differential Forms
论文作者
论文摘要
我们使用有限元外积分作为统一框架的矢量值有限元方法的近似理论中的基本方面。我们将克莱门特插入术和斯科特 - 宗室内固体概括为有限的元素差异形式，并得出了破碎的紫红色 - 希尔伯特·莱姆玛（Bramble-Hilbert Lemma）。我们的插值仅需要最小的平滑度假设并尊重部分边界条件。这使我们可以根据网格大小陈述本地错误估计。我们的理论结果适用于简单三角剖分的卷曲构成和构成差异有限元方法。
We address fundamental aspects in the approximation theory of vector-valued finite element methods, using finite element exterior calculus as a unifying framework. We generalize the Clément interpolant and the Scott-Zhang interpolant to finite element differential forms, and we derive a broken Bramble-Hilbert Lemma. Our interpolants require only minimal smoothness assumptions and respect partial boundary conditions. This permits us to state local error estimates in terms of the mesh size. Our theoretical results apply to curl-conforming and divergence-conforming finite element methods over simplicial triangulations.
