First-Order System Least Squares for the Signorini Contact Problem in Linear Elasticity

A first-order system least squares formulation for the Signorini problem modeling frictionless contact in linear elasticity is studied. In addition to the displacement field, the stress tensor is used as an independent process variable. A contact boundary term is added to the usual least squares functional in order to achieve coercivity and continuity in appropriate norms. The discrete functional is shown to constitute an a posteriori error estimator on which an adaptive refinement strategy may be based. As finite element spaces, standard conforming piecewise polynomials for the displacement approximation are combined with Raviart–Thomas elements for the rows in the stress tensor. Computational results for a test problem of Hertzian contact illustrate the effectiveness of our least squares approach.