Numerical verification of solutions for some unilateral boundary value problems

In this paper, we consider a numerical technique which enables us to verify the existence of solutions for some unilateral boundary value problems. Using the finite element approximations and explicit a priori error estimates, we construct, in a computer, a set of solutions which satisfies the hypothesis of Schauderʹs fixed-point theorem for a compact map on a certain Sobolev space. Further, the conditions of verifiability by this method are considered and some numerical examples are presented.