Gradient Robust Mixed Methods for Nearly Incompressible Elasticity

Abstract Within the last years pressure robust methods for discretization of incompressible fluids have been developed. These allow use standard finite elements solution problem while simultaneously removing a spurious influence in approximation error velocity fluid, or displacement an solid. To this end, reconstruction operators are utilized mapping discretely divergence free functions to functions. This work shows that modifications proposed Stokes equation by Linke (Comput Methods Appl Mech Eng 268:782–800, 2014) also yield gradient nearly elastic materials without need resort discontinuous as Fu et al. (J Sci Comput 86(3):39–30, 2021).