Gradient Schemes for an Obstacle Problem

Abstract The aim of this work is to adapt the gradient schemes, discretisations of weak variational formulations using independent approximations of functions and gradients, to obstacle problems modelled by linear and non-linear elliptic variational inequalities. It is highlighted in this paper that four properties which are coercivity, consistency, limit conformity and compactness are adequate to ensure the conver-gence of this scheme. Under some suitable assumptions, the error estimate for linear equations is also investigated