Speaker
Description
In this contribution, we present a novel three-field finite element for the Stokes eigenvalue problem. To this end, we approximate the Hellinger-Reissner (mixed) formulation where the symmetry of the stress tensor σ is dealt with in a weak form by introducing a Lagrange multiplier that represents the conservation of angular momentum. We consider the space of tensors whose rows consist of an element of RT space for the stress, the space of discontinuous piecewise linear vectors for the velocity, and the space of skew-symmetric continuous piecewise linear tensors to impose the symmetry weakly. We end up with a stress-velocity-vorticity formulation discretized with RTₖᵈ−DPₖᵈ−Pₖ^ {d (d−1)/2} with k ≥ 1. This formulation has notable benefits, as it directly arises from the fundamental physical principles of momentum balance, constitutive law, and mass conservation. Moreover, it provides a direct presentation of stress, which is particularly crucial in certain applications. Numerical examples in both convex and non-convex two and three dimensional domains are presented to illustrate the efficiency of the proposed methodology.
