Efficient and reliable a posteriori error estimators for elliptic obstacle problems

A posteriori error estimators are derived for linear finite element approximations to elliptic obstacle problems. These estimators yield global upper and local lower bounds for the discretization error. Here discretization error means the sum of two contributions: the distance between continuous and discrete solution in the energy-norm and some quantity that is related to the distance of continuous and discrete contact set. Moreover, the local error indicators in the interior of the discrete contact set reduce to quantities that measure only data resolution.