Enclosure of solutions of weakly nonlinear elliptic boundary value problems and their computation

An algorithm is presented to compute approximations as well as continuous bounds for solutions of weakly nonlinear elliptic boundary value problems. The given problem is majorized in some sense and the obtained new problem is solved by a finite element method. The finite element solution is computed by a monotone iteration process and at last transformed to a continuous (lower) bound for a solution. Convergence is proved and mesh refinement effects are discussed. Two numerical examples are given.