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 deal with the goal-oriented error estimates and mesh adaptation for nonlinear partial
differential equations. The setting of the adjoint problem and the resulting estimates are not …

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 a second-order elliptic boundary value problem with strongly monotone and
Lipschitz-continuous nonlinearity. We design and study its adaptive numerical …

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 …

We consider a general nonsymmetric second-order linear elliptic partial differential equation
in the framework of the Lax–Milgram lemma. We formulate and analyze an adaptive finite …

The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to
compute an approximation of user-prescribed accuracy at quasi-minimal computational …

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 …