On the application of a global post-processing strategy for stress recovery in nearly-incompressible elasticity problems

Resumo

In the context of linear elasticity problems, the two major variables to be determined are the displace-
ment and the stress tensor fields, which are often required in real-world applications. However, some classical and

widely used finite element methods for these problems only provide approximations for the displacement, and the
stress tensor needs to be post-processed. In this work, we study a post-processing strategy for the stress recovery
obtained by combining the weak form of the constitutive equation with a least-square residual of the equilibrium
equation. We will focus our studies on the application of this post-processing strategy in elasticity problems with

nearly-incompressible materials, which are known in the literature to offer additional challenges. Providing an ac-
curate approximation for the displacement field, our main goal is to evaluate whether the post-processing strategy

is able to obtain satisfactory approximations for the stress tensor field on nearly-incompressible problems.