Finite element error estimates in non-energy norms for the two-dimensional scalar Signorini problem

This paper is concerned with error estimates for the piecewise linear finite element approximation of the two-dimensional scalar Signorini problem on a convex polygonal domain omega Using a Cea-type lemma, a supercloseness result, and a non-standard duality argument, we proveW1,p(omega)\,L infinity(omega)\,W1,infinity(omega)-, andH1/2( partial differential omega)-error estimates under reasonable assumptions on the regularity of the exact solution andLp(omega)-error estimates under comparatively mild assumptions on the involved contact sets. The obtained orders of convergence turn out to be optimal for problems with essentially bounded right-hand sides. Our results are accompanied by numerical experiments which confirm the theoretical findings.