论文标题
多边形网格上的任意订购离散腐烂旋转复合物，并应用于四轮问题
An arbitrary-order discrete rot-rot complex on polygonal meshes with application to a quad-rot problem
论文作者
论文摘要
在这项工作中，遵循离散的DE RHAM（DDR）方法，我们开发了具有增强规律性的二维DE RHAM复合物的离散对应物。拟议的建筑支持一般的多边形网格和任意近似顺序。我们在具有和没有边界条件的复合物的两个版本上建立了合理的域名，并且对于前者来说，证明了一套庞加莱型的不平等。然后，使用离散复合物来得出四轮问题的新型离散方法，该方法与文献中的其他方案不同，不需要准备强迫项。我们对拟议方案进行完全稳定和收敛分析，并提供结果的数值验证。
In this work, following the discrete de Rham (DDR) approach, we develop a discrete counterpart of a two-dimensional de Rham complex with enhanced regularity. The proposed construction supports general polygonal meshes and arbitrary approximation orders. We establish exactness on a contractible domain for both the versions of the complex with and without boundary conditions and, for the former, prove a complete set of Poincaré-type inequalities. The discrete complex is then used to derive a novel discretisation method for a quad-rot problem which, unlike other schemes in the literature, does not require the forcing term to be prepared. We carry out complete stability and convergence analyses for the proposed scheme and provide numerical validation of the results.
