A novel hierarchial error estimate for elliptic obstacle problems (Q1936321)

The author considers the following symmetric, elliptic obstacle problem: \[ \text{Find }u\in K\text{ such that } a(u,v- u)\geq(f,v- u)\,\forall v\in K, \] where \(a(.,.)\) is a bilinear form defined by \[ a(v,w)= \int_\Omega\nabla v\cdot\nabla w,\quad v,w\in H^1_0(\Omega). \] For this problem, the author presents and analyzes a novel hierarchical a posteriori error estimate. The main result is that the energy norm of the finite elemene approximate error is, up to some extra oscillation term, equivalent to an appropriate hierarchical estimator. -- Some numerical experiments are given.