When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

The mathematical theory of Krylov subspace methods with a focus on solving systems of
linear algebraic equations is given a detailed treatment in this principles-based book …

Solving systems of algebraic linear equations is among the most frequent problems in
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …

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

We prove convergence with optimal algebraic rates for an adaptive finite element method for
nonlinear equations with strongly monotone operator. Unlike prior works, our analysis also …

This paper presents a methodology for computing upper and lower bounds for both the
algebraic and total errors in the context of the conforming finite element discretization of the …

Abstract The Adaptive Finite Element Method (AFEM) for approximating solutions of PDE
boundary value and eigenvalue problems is a numerical scheme that automatically and …

We present novel H (div) and H 1 liftings of given piecewise polynomials over a hierarchy of
simplicial meshes, based on a global solve on the coarsest mesh and on local solves on …