Numerical verification of solutions for nonlinear elliptic problems using an L∞ residual method

We consider a numerical enclosure method with guaranteed L-infinity error bounds for the solution of nonlinear elliptic problems of second order. By using an a posteriori error estimate for the approximate solution of the problem with a higher order C-0-finite element, it is shown that we can obtain the guaranteed L-infinity error bounds with high accuracy, A particular emphasis is that our method needs no assumption of the existence of the solution of the original nonlinear equation, but it follows as the result of computation itself. A numerical example that confirms the effectiveness of the method is presented. (C) 1998 Academic Press.