This paper reviews the state of the art and discusses recent developments in the field of
adaptive isogeometric analysis, with special focus on the mathematical theory. This includes …

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 …

In this work, we formulate and analyze a geometric multigrid method for the iterative solution
of the discrete systems arising from the finite element discretization of symmetric second …

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 …

The convergence analysis for least-squares finite element methods led to various adaptive
mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori …

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 …

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 consider numerical approximations of nonlinear, monotone, and Lipschitz-continuous
elliptic problems, with gradient-dependent or gradient-independent diffusivity. For this …