Niveau: Supérieur, Doctorat, Bac+8
A stabilized Lagrange multiplier method for the finite element approximation of contact problems in elastostatics Patrick Hild1, Yves Renard2 Abstract In 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. Key words: unilateral contact, finite elements, mixed method, stabilization, a priori error estimate. Abbreviated title: Stabilized Lagrange multiplier method for contact problems Mathematics subject classification: 65N30, 74M15 1 Introduction and notation The numerical implementation of contact and impact problems in solid mechanics generally uses finite element tools (see [22, 24, 29, 38, 39, 48]). An important aspect in these simulations consists of choosing finite element methods which are both easy to implement in practice and accurate from a theoretical point of view. Our aim in this paper is to propose, study and discuss the performances of such a method. In order to focus only on the nonlinearity arising from the unilateral contact problem, we consider in what follows the simplest model: linear elasticity, small strains and no friction.
- describing unilateral
- any µh ?
- contact condition
- vh
- µh ?
- convex cone
- strictly convex
- ?c ?