A priori error for unilateral contact problems with augmented Lagrange multipliers and IsoGeometric Analysis

The aim of the present work is to extend the a priori error for contact problems with an augmented Lagrangian method. We focus on unilateral contact problem without friction between an elastic body and a rigid one. We consider the pushforward of a NURBS space of degree $p$ for the displacement and the pushforward of a B-Spline space of degree $p-2$ for the Lagrange multipliers. This specific choice of space is a stable couple of spaces. An optimal a priori error estimate inspired from the Nitsche's method theory is provided and compared to the regularity of the solution. We perform a numerical validation with two- and three-dimensions in small and large deformations with $N2/S0$ and $N3/S1$ elements.