论文标题
混合高阶方案中的扩散各向异性和网状偏度之间的相互作用
Interplay between diffusion anisotropy and mesh skewness in Hybrid High-Order schemes
论文作者
论文摘要
我们探讨了网格偏度对各向异性扩散方程的标准混合高阶（HHO）方案的准确性的影响。在定义了规则偏斜序列的概念之后，例如对于在网格细化过程中变得越来越伸长的元素，我们建立了一个误差估计值，在该元素中，我们可以准确地以扩散张量和网状链条来精确地跟踪局部多重常数的依赖性。这种依赖性使显式在局部扩散属性与元素的失真之间存在相互作用。然后，我们提供了几个数值结果，以评估高度各向异性扩散或高度扭曲的网格的HHO的实际收敛特性。这些测试表明的行为比理论估计值表明的行为更强大。
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.
