Solving obstacle problems with guaranteed accuracy

In this paper, we consider a numerical technique which enables us to verify the existence of solutions for some simple obstacle problems. Using the finite element approximation and constructive error estimates, we construct, on a computer, a set of solutions which satisfies the hypothesis of the Schauder fixed-point theorem for a compact map on a certain Sobolev space. We describe the numerical verification algorithm for solving a two-dimensional obstacle problems and report some numerical results.