混合高阶格式中扩散各向异性与网格偏斜的相互影响
Interplay between diffusion anisotropy and mesh skewness in Hybrid High-Order schemes
摘要：
研究了网格偏斜度对求解各向异性扩散方程的标准混合高阶（HHO）格式精度的影响。在定义了规则偏斜网格序列的概念之后，这允许，例如，对于在网格细化过程中变得越来越细长的单元，我们建立了一个误差估计，其中我们精确地跟踪了局部乘法常数在扩散张量和网格偏斜度方面的依赖性。这种依赖性使得明确的局部扩散属性和元素的失真之间的相互作用。然后，我们提供了几个数值结果来评估实际的收敛性能的HHO高度各向异性扩散或高度扭曲的网格。这些测试表明比理论估计值更稳健的行为。
英文摘要：
We explore the effects of mesh skewness on the accuracy of standard Hybrid High-Order (HHO) schemes for anisotropic diffusion equations. After defining a notion of regular skewed mesh sequences, which allows, e.g., for elements that become more and more elongated during mesh refinement, we establish an error estimate in which we precisely track the dependency of the local multiplicative constants in terms of the diffusion tensor and mesh skewness. This dependency makes explicit an interplay between the local diffusion properties and the distortion of the elements. We then provide several numerical results to assess the practical convergence properties of HHO for highly anisotropic diffusion or highly distorted meshes. These tests indicate a more robust behaviour than the theoretical estimate indicates.
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