论文标题
三维混合空间的离散韦伯不等式，并应用于磁静态的HHO近似
A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of magnetostatics
论文作者
论文摘要
我们证明了第一个Weber不等式的离散版本在三维混合空间上，该空间由附着在多面部网格的元素和面上的多项式载体跨越。然后，我们在其（一阶）场和（二阶）矢量电位配方中引入了两种混合高阶方法，以供磁静态模型的近似值。这些方法适用于一般的多面体网格，并允许任意近似阶。利用先前建立的离散Weber不平等，我们对这两种方法进行全面分析。我们最终在一组测试箱上验证了它们。
We prove a discrete version of the first Weber inequality on three-dimensional hybrid spaces spanned by vectors of polynomials attached to the elements and faces of a polyhedral mesh. We then introduce two Hybrid High-Order methods for the approximation of the magnetostatics model, in both its (first-order) field and (second-order) vector potential formulations. These methods are applicable on general polyhedral meshes, and allow for arbitrary orders of approximation. Leveraging the previously established discrete Weber inequality, we perform a comprehensive analysis of the two methods. We finally validate them on a set of test-cases.
