Numerical verification of solutions for obstacle problems. (Q1421206)

The authors follow the approach of their previous paper [Numer. Math. 81, 305--320 (1998; Zbl 0919.65043)] and develop a method for verifying existence of solutions for a more general class of nonlinear obstacle problems, which can be represented as a variational inequality involving a bilinear form and a general continuous operator. The method is based upon a suitable finite element approximation and a derivation of a priori estimates for direct verification of conditions of Schauder's fixed point theorem.