On a two-field finite element approximation in elasticity

In this paper relatively well-known two-field (mixed) finite element approximations in the mechanics of solids are studied. However, in the proposed approach a significant novelty (in the finite element methods) is introduced – the treatment of the boundary traction constraints as essential boundary conditions. Although multifield approximations are in no way limited to the realm of classical elasticity, to fix ideas we are considering the linear elastic domain, where the comparable analytical solutions are available.