Finite element spaces on a tetrahedron are constructed for $\operatorname
{div}\operatorname {div} $-conforming symmetric tensors in three dimensions. The key tools …

A finite element elasticity complex on tetrahedral meshes and the corresponding
commutative diagram are devised. The $ H^ 1$ conforming finite element is the finite …

This paper introduces a new family of mixed finite elements for solving a mixed formulation
of the biharmonic equations in two and three dimensions. The symmetric stress σ=−∇ 2 u is …

In this work we address the reduction of face degrees of freedom (DOFs) for discrete
elasticity complexes. Specifically, using serendipity techniques, we develop a reduced …

A new $ H (\operatorname {div}\operatorname {div}) $-conforming finite element is
presented, which avoids the need for supersmoothness by redistributing the degrees of …

Two types of finite element spaces on a tetrahedron are constructed for divdiv conforming
symmetric tensors in three dimensions. The key tools of the construction are the …

We construct finite element approximations of the Levi-Civita connection and its curvature on
triangulations of oriented two-dimensional manifolds. Our construction relies on the Regge …

We construct conforming finite element elasticity complexes on Worsey–Farin splits in three
dimensions. Spaces for displacement, strain, stress, and the load are connected in the …

We construct conforming finite element elasticity complexes on the Alfeld splits of tetrahedra.
The complex consists of vector fields and symmetric tensor fields, interlinked via the …

In this study, two-dimensional finite element complexes with various levels of smoothness,
including the de Rham complex, the curldiv complex, the elasticity complex, and the divdiv …