论文标题
关于差分形式的准多物质空间的Unisovence
On the unisolvence for the quasi-polynomial spaces of differential forms
论文作者
论文摘要
我们认为差分形式的准多项式空间定义为具有多项式系数的差分形式的加权（正权重）空间。我们表明，在任何空间尺寸上，在单纯尺寸上的此类空间的统一功能集与用于多项式空间的此类功能集相同。但是，准多项式空间中的分析不是标准配置，并且需要一种新颖的方法。我们能够在不使用Stokes定理的情况下证明我们的结果，这是显示差分形式多项式空间中功能的一致性的标准工具。这些新结果为研究指数拟合的离散化提供了工具，可用于希尔伯特差异复合物中的一般对流扩散问题稳定。
We consider quasi-polynomial spaces of differential forms defined as weighted (with a positive weight) spaces of differential forms with polynomial coefficients. We show that the unisolvent set of functionals for such spaces on a simplex in any spatial dimension is the same as the set of such functionals used for the polynomial spaces. The analysis in the quasi-polynomial spaces, however, is not standard and requires a novel approach. We are able to prove our results without the use of Stokes' Theorem, which is the standard tool in showing the unisolvence of functionals in polynomial spaces of differential forms. These new results provide tools for studying exponentially-fitted discretizations stable for general convection-diffusion problems in Hilbert differential complexes.
