Locking-free finite element approximations for a parameter-dependent variational inequality

Abstract

We present two robust finite element approximations for the unilateral contact problem of a Timoshenko beam. The two numerical approximations are based on conforming methods with dual Lagrange multipliers. The first uses a suitable stable pair of finite element spaces. The second is a stabilized formulation that allows the use of standard low-order finite element spaces. A priori and a residual posteriori error estimates are derived. Comprehensive numerical tests that validate and illustrate our approach are also given.