Recently $C^m$-conforming finite elements on simplexes in arbitrary dimension are constructed by Hu, Lin and Wu. The key in the construction is a non-overlapping decomposition of the simplicial lattice in which each component will be used to determine the normal derivatives at each lower dimensional sub-simplex. A geometric approach is proposed in this paper and a geometric decomposition of the finite element spaces is given. Our geometric decomposition using the graph distance not only simplifies the construction but also provides an easy way of implementation.
翻译:最近,胡、林和吴建造了胡、林和吴在任意尺寸的简单氧化物上符合要求的限定元素。建设的关键是,不重叠地分解简化板,其中每个组件将被用来确定每个低维次质的正常衍生物。本文提出了几何方法,并给出了有限元素空间的几何分解。我们使用图形距离的几何分解不仅简化了构建过程,而且提供了简单的实施方法。