论文标题
实现一般虚拟元素空间的框架
A framework for implementing general virtual element spaces
论文作者
论文摘要
在本文中，我们提出了一个基于由约束最小二乘问题构建的预测的一般虚拟元素空间构建和实施的框架。在用于有限元元素空间的三元组的基础上，我们介绍了VEM元组的概念，该概念编码了必要的构建块来构建这些预测。使用这种方法，可以定义广泛的虚拟元素空间。我们讨论了$ h^k $ - 以$ k = 1,2 $以及差异和弯曲空间的配合空间。该一般框架的优点是可以轻松地集成到任何现有的有限元包中，我们将其在开源软件包沙丘中演示。
In this paper we present a framework for the construction and implementation of general virtual element spaces based on projections built from constrained least squares problems. Building on the triples used for finite element spaces, we introduce the concept of a VEM tuple which encodes the necessary building blocks to construct these projections. Using this approach, a wide range of virtual element spaces can be defined. We discuss $H^k$-conforming spaces for $k=1,2$ as well as divergence and curl free spaces. This general framework has the advantage of being easily integrated into any existing finite element package and we demonstrate this within the open source software package DUNE.
