论文标题
用于对称的对称张量的有限元素
Finite elements for divdiv-conforming symmetric tensors
论文作者
论文摘要
三角形上的两种有限元空间是用于Div-Div符合对称张量的两种有限元空间。除了正常的连续性外，应力张量在顶点处是连续的，并且还鉴定了涉及应力衍生物组合的另一个痕迹。提出了多项式复合物，有限元复合物和希尔伯特复合物，并给出了它们之间的通勤图。利用构造的Div-Div符合元素来离散Biharmonic方程的混合配方。提供了最佳订单和超授权误差分析。通过旋转，还获得了腐烂构象对称应变的有限元。
Two types of finite element spaces on triangles are constructed for div-div conforming symmetric tensors. Besides the normal-normal continuity, the stress tensor is continuous at vertices and another trace involving combination of derivatives of stress is identified. Polynomial complex, finite element complex, and Hilbert complex are presented and a commuting diagram between them is given. The constructed div-div conforming elements are exploited to discretize the mixed formulation of the biharmonic equation. Optimal order and superconvergence error analysis is provided. By rotation, finite elements for rot-rot conforming symmetric strain are also obtained.
