Inexact monotone methods for solving nonlinear elliptic problems

Abstract

We numerically solving semilinear elliptic problems with the method of upper and lower solutions. Inexact monotone iterative methods are constructed, where monotone linear systems are solved by the Jacobi or Gauss-Seidel methods only approximately. The inexact monotone methods combine the quadratic monotone iterative method at outer iterations and the Jacobi or Gauss-Seidel methods at inner iterations, and possess global monotone convergence. Results of numerical experiments are presented.