Pointwise superconvergence of recovered gradients for piecewise linear finite element approximations to problems of planar linear elasticity

In this paper we consider piecewise linear finite element approximations to the problem of planar linear elasticity, and present some new estimates for the pointwise (L_∞) superconvergence of a recovered gradient function to the gradient of the true solution. This extends to linear elasticity the previous work of the present and other authors on L_∞ results for Poisson problems, and at the same time, to the L_∞ norm the previous L₂ results of the authors for linear elasticity.