We formulate and analyze a goal-oriented adaptive finite element method for a semilinear
elliptic PDE and a linear goal functional. The discretization is based on finite elements of …

We revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert
spaces. Our key observation is that the general approach from [P. Heid and TP Wihler …

We consider adaptive finite element methods for second-order elliptic PDEs, where the
arising discrete systems are not solved exactly. For contractive iterative solvers, we …

We present an effective adaptive procedure for the numerical approximation of the steady-
state Gross–Pitaevskii equation. Our approach is solely based on energy minimization, and …

We consider scalar semilinear elliptic PDEs where the nonlinearity is strongly monotone, but
only locally Lipschitz continuous. We formulate an adaptive iterative linearized finite element …

A wide variety of (fixed-point) iterative methods for the solution of nonlinear equations (in
Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative local …

A wide variety of different (fixed-point) iterative methods for the solution of nonlinear
equations exists. In this work we will revisit a unified iteration scheme in Hilbert spaces from …

In this article we investigate the use of fixed point iterations to solve the Galerkin
approximation of strictly monotone problems. As opposed to Newton's method, which …

In this paper, the virtual element method is employed to approximate semilinear elliptic
problems over arbitrary polygonal meshes. The nonlinear load term is approximated by …

We present a novel energy-based numerical analysis of semilinear diffusion-reaction
boundary value problems, where the nonlinear reaction terms need to be neither monotone …