Hybrid finite element methods for the Signorini problem

We study three mixed linear finite element methods for the numerical simulation of the two-dimensional Signorini problem. Applying Falk’s Lemma and saddle point theory to the resulting discrete mixed variational inequality allows us to state the convergence rate of each of them. Two of these finite elements provide optimal results under reasonable regularity assumptions on the Signorini solution, and the numerical investigation shows that the third method also provides optimal accuracy.