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.