论文标题
有限的元素de rham并在三个维度
Finite Element de Rham and Stokes Complexes in Three Dimensions
论文作者
论文摘要
有限元元素de rham复合物和有限元在三维中具有各种平滑度的配合物是系统地构建的。三个维度中的第一个平滑标量有限元通过简单晶格的非重叠分解得出。基于平滑的标量有限元，h（div）合并有限元和h（curl）合并具有各种平滑度的有限元元素，这些元素具有各种平滑度，这会诱导具有各种平滑度和相关交换图的有限元元素DE RHAM复合物。 DIV稳定性是针对H（div）合并有限元素的，以及这些有限元复合物的精确性。
Finite element de Rham complexes and finite element Stokes complexes with various smoothness in three dimensions are systematically constructed. First smooth scalar finite elements in three dimensions are derived through a non-overlapping decomposition of the simplicial lattice. Based on the smooth scalar finite elements, both H(div)-conforming finite elements and H(curl)-conforming finite elements with various smoothness are devised, which induce the finite element de Rham complexes with various smoothness and the associated commutative diagrams. The div stability is established for the H(div)-conforming finite elements, and the exactness of these finite element complexes.
