Mesh independent superlinear convergence of an inner–outer iterative method for semilinear elliptic interface problems

摘要

We propose the damped inexact Newton method, coupled with preconditioned inner iterations, to solve the finite element discretization of a class of nonlinear elliptic interface problems. The linearized equations are solved by a preconditioned conjugate gradient method. Both the inner and outer iterations exhibit mesh independent superlinear convergence.