  Variational phase-field models of fracture are widely used to simulate
nucleation and propagation of cracks in brittle materials. They are based on
the approximation of the solutions of free-discontinuity fracture energy by two
smooth function: a displacement and a damage field. Their numerical
implementation is typically based on the discretization of both fields by nodal
$\mathbb{P}^1$ Lagrange finite elements. In this article, we propose a
nonconforming approximation by discontinuous elements for the displacement and
nonconforming elements, whose gradient is more isotropic, for the damage. The
handling of the nonconformity is derived from that of heterogeneous diffusion
problems. We illustrate the robustness and versatility of the proposed method
through series of examples.

Numerical Analysis;Numerical Analysis;Analysis of PDEs