Convergence rates for the classical, thin and fractional elliptic   obstacle problems
  We review the finite element approximation of the classical obstacle problem in energy and max-norms and derive error estimates for both the solution and the free boundary. On the basis of recent regularity results we present an optimal error analysis for the thin obstacle problem. Finally, we discuss the localization of the obstacle problem for the fractional Laplacian and prove quasi-optimal convergence rates. 
Ricardo H. Nochetto and Enrique Ot\'arola and Abner J. Salgado
math.NA