Solving Nonlinear Elliptic Problems with Result Verification Using an H -1 Type Residual Iteration

Solving Nonlinear Elliptic Problems with Result Verification Using anH-1Type Residual Iteration. In this paper, we consider a numerical technique to verify the solutions with guaranteed error bounds for nonlinear elliptic boundary value problems. Using the C° finite element solution and explicit error estimates for the Poisson equation, we construct, in a computer, a set of functions which satisfies the hypothesis of Sadovskii’s fixed point theorem for confdensing map on a certain Sobolev space. Particularly, we propose an H-1 type residual iteration method which improves the ability of verification. A numerical example which confirms the usefulness of the method is presented.