Several div-conforming and divdiv-conforming finite elements for symmetric tensors on simplexes in arbitrary dimension are constructed in this work. The shape function space is first split as the trace space and the bubble space. The later is further decomposed into the null space of the differential operator and its orthogonal complement. Instead of characterization of these subspaces of the shape function space, characterization of the duals spaces are provided. Vector div-conforming finite elements are firstly constructed as an introductory example. Then new symmetric div-conforming finite elements are constructed. The dual subspaces are then used as build blocks to construct divdiv conforming finite elements.
翻译:在这项工程中构建了在任意维度的简单氧化物上对称式抗拉的多个 div-conform-div-confization 限定元素。形状功能空间首先作为跟踪空间和气泡空间分割。后又进一步分解成差分操作器的空格及其正方形补充。提供了对形状功能空间的这些子空间的定性,而不是对形状功能空间的这些子空间的定性。矢量 div-conformiz-conform 有限元素首先作为介绍性示例进行构建。然后又构建了新的对称式 div-conformization有限元素。然后,将双面子空间用作构建符合 divdiv 的固定元素的建筑块。