Variable preconditioning for strongly nonlinear elliptic problems (Q1713163)

The paper is concerned with variable preconditioning for the iterative solution of strongly nonlinear elliptic problems. First, the authors study a class of operator equations with unbounded nonlinearities and then they focus on elliptic problems with power order nonlinearities. They use the finite element method for the discretization of elliptic problems and the quasi-Newton method for discretized problems. The Gâteaux derivative of the operator is approximated by a spectrally equivalent linear operator which enables variable preconditioning. The authors prove the convergence of the method. Numerical experiments are presented to confirm the theoretical results.