The Adaptive Nonconforming FEM for the Pure Displacement Problem in Linear Elasticity is Optimal and Robust

This paper presents a natural nonconforming adaptive finite element algorithm and proves its quasi-optimal complexity for the pure displacement Navier–Lame equations. The convergence rates are robust with respect to the Lame parameter $\lambda \to \infty$ in the sense that all constants in the quasi-optimal convergence rate stay bounded for almost incompressible materials and so the Stokes equations are covered by our analysis in the limit $\lambda = \infty$.