Zoom id：941 567 2172

密码：20201315

Two types of finite element spaces on triangles and tetrahedrons are constructed for div-div conforming symmetric tensors in two and three dimensions. Besides the normal-normal component, another trace involving combination of first order derivatives of stress should be continuous across the sides of the element. Due to the rigid of polynomials, the stress tensor element is also continuous at vertices, and on the plane orthogonal to each edge in three dimensions. Hilbert complex and polynomial complexes are presented and several decomposition of polynomial vector and tensors spaces are revealed from the complexes. 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. The standard Lagrange element basis can be used to implement the hybridized formulation.

This is a joint work with Xuehai Huang from Shanghai University of Finance and Economic.