Abstract:

We consider scalar semilinear elliptic PDEs where the nonlinearity is strongly monotone, but only locally Lipschitz continuous. The proposed adaptive iteratively linearized finite element method (AILFEM) steers the local mesh refinement and the iterative linearization of the arising nonlinear discrete equations. As a means of linearization, we employ a damped Zarantonello iteration so that, in each step of the algorithm, only a linear Poisson-type equation has to be solved. We present the two main results: First, full linear convergence, i.e., contraction for each step of the algorithm whether it is a discretization step or a linearization step. Second, rate-optimality of the proposed algorithm, i.e., optimal convergence rates understood with respect to an idealized computational cost.

This event takes place in hybrid form (in person and online on Zoom). Slides and additional materials are available on the Moodle service of the University of Vienna. If you want to participate, please write an email to matteo.tommasini@univie.ac.at. Further details are available at this link.