Finite Elements for Signorini

This chapter is devoted to the finite element approximation of the Signorini problem ( 3.12 ) described in previous Chap. 3 . We start with the simplest possible setting just to point out the main difficulty that appears in the convergence analysis of many methods. We then present discretizations based on a direct approximation of the variational inequality ( 3.12 ), with different alternatives to build discrete convex cones that approximate K. After this, we focus on the derivation of optimal a priori error estimates in the natural H 1-norm related to the approximate solution.