Mixed finite elements of higher-order in elastoplasticity

In this paper a higher-order mixed finite element method for elastoplasticity with linear kinematichardening is analyzed. Thereby, the non-differentiability of the involved plasticity functionalis resolved by a Lagrange multiplier leading to a three field formulation. The finite elementdiscretization is conforming in the displacement field and the plastic strain but potentially non-conforming in the Lagrange multiplier as its Frobenius norm is only constrained in a certain setof Gauss quadrature points. A discrete inf-sup condition with constant 1 and the well posednessof the discrete mixed problem are shown. Moreover, convergence and guaranteed convergencerates are proved with respect to the mesh size and the polynomial degree, which are optimal forthe lowest order case. Numerical experiments underline the theoretical results.