We introduce a novel relaxed Kačanov scheme for the computation of the discrete minimizer
to the-Laplace problem with. The iterative scheme is easy to implement since each iterate …

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 nonsmooth partial differential equations associated with a minimization of an
energy functional. We adaptively regularize the nonsmooth nonlinearity so as to be able to …

Most adaptive finite element strategies employ the Dörfler marking strategy to single out
certain elements $\mathcal {M}\subseteq\mathcal {T} $ of a triangulation $\mathcal {T} $ for …

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 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 …

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 …