A mixed finite element for weakly-symmetric elasticity
This provides a new stable and optimal finite element discretization for linear elasticity, which is important for computational mechanics.
The paper develops a mixed finite element for weakly-symmetric elasticity on tetrahedral meshes, proving stability and optimal approximation properties for the triplet of spaces. The lowest order case yields a compact cell-centered finite volume scheme for displacement.
We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement, $H(\mathrm{div})$-conforming polynomials of order $r+1$ for the stress, and $H(\mathrm{curl})$-conforming polynomials of order $r+1$ for the vector representation of the multiplier. We prove that this triplet is stable and has optimal approximation properties. The lowest order case can be combined with inexact quadrature to eliminate the stress and multiplier variables, leaving a compact cell-centered finite volume scheme for the displacement.