We present a parallel data structure for the discretization of partial differential equations which is based on distributed point objects and which enables the flexible, transparent, and efficient realization of conforming, nonconforming, and mixed finite elements. This concept is realized for elliptic, parabolic and hyperbolic model problems, and sample applications are provided by a tutorial complementing a lecture on scientific computing.

The corresponding open-source software is based on this parallel data structure, and it supports multilevel methods on nested meshes and 2D and 3D as well as in space–time. Here, we present generic results on porous media applications including multilevel preconditioning and multilevel Monte Carlo methods for uncertainty quantification.

我们提出了一种用于偏微分方程离散化的并行数据结构，该结构基于分布点对象，并且能够灵活，透明且有效地实现符合，不符合和混合有限元。这个概念是针对椭圆，抛物线和双曲线模型问题而实现的，示例应用程序由与科学计算讲座互补的教程提供。

相应的开源软件基于此并行数据结构，并且支持嵌套网格，2D和3D以及时空上的多层方法。在这里，我们介绍了多孔介质应用的一般结果，包括用于不确定性量化的多级预处理和多级蒙特卡洛方法。