A stabilized Lagrange multiplier method for the finite element approximation of contact problems in elastostatics

International audienceIn this work we consider a stabilized Lagrange (or Kuhn-Tucker) multiplier method in order to approximate the unilateral contact model in linear elastostatics. The particularity of the method is that no discrete inf-sup condition is needed in the convergence analysis. We propose three approximations of the contact conditions well adapted to this method and we study the convergence of the discrete solutions. Several numerical examples in two and three space dimensions illustrate the theoretical results and show the capabilities of the method