Javier A. Almonacid, Gabriel N. Gatica, Ricardo Ruiz-Baier:
Ultra-weak symmetry of stress for augmented mixed finite element formulations in continuum mechanics
In this paper, we describe a novel way to prescribe weakly the symmetry of stress tensors in weak formulations. The approach is first introduced in the context of solid mechanics (using the linear elasticity problem, for simplicity purposes), and then we apply this technique to reduce the computational cost of an augmented fully-mixed method in fluid mechanics where several additional variables are defined. We show that the analysis can be carried out in the same terms as in their original works, and therefore, we only focus on the coercivity of bilinear forms, as this property provides feasible ranges for the stabilization parameters that complete the description of augmented methods. In addition, we present some numerical examples to show that these methods perform better than their counterparts that include vorticity, as the reduction in degrees of freedom (and therefore, in computational cost) does not affect the quality of numerical solutions.