A NEW MIXED FINITE ELEMENT FOR THE LINEAR ELASTICITY PROBLEM IN 3D

This paper constructs the first mixed finite element for the linear elasticity problem in 3D using P₃ polynomials for the stress and discontinuous P₂ polynomials for the displace-ment on tetrahedral meshes under some mild mesh conditions. The degrees of freedom of the stress space as well as the corresponding nodal basis are established by characterizing a space of certain piecewise constant symmetric matrices on a patch around each edge. Macro-element techniques are used to define a stable interpolation to prove the discrete inf-sup condition. Optimal convergence is obtained theoretically.