三维杂交空间上离散的Weber不等式及其在静磁学HHO近似中的应用
A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of magnetostatics
摘要：
我们证明了一个离散版本的第一韦伯不等式的三维混合空间上的多项式向量连接到多面体网格的元素和面。然后，我们介绍了两个混合高阶方法的近似的静磁模型，在其（一阶）场和（二阶）矢量位配方。这些方法适用于一般的多面体网格，并允许任意阶的近似。利用先前建立的离散Weber不等式，我们对这两种方法进行了全面的分析。最后，我们在一组测试用例上验证了它们。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
