Energy contraction and optimal convergence of adaptive iterative linearized finite element methods
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 …
spaces. Our key observation is that the general approach from [P. Heid and TP Wihler …
Rate optimality of adaptive finite element methods with respect to overall computational costs
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 …
arising discrete systems are not solved exactly. For contractive iterative solvers, we …
[HTML][HTML] Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation
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 …
state Gross–Pitaevskii equation. Our approach is solely based on energy minimization, and …
[HTML][HTML] Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver
A Haberl, D Praetorius, S Schimanko… - Numerische Mathematik, 2021 - Springer
We consider a second-order elliptic boundary value problem with strongly monotone and
Lipschitz-continuous nonlinearity. We design and study its adaptive numerical …
Lipschitz-continuous nonlinearity. We design and study its adaptive numerical …
Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs
R Becker, M Brunner, M Innerberger… - ESAIM: Mathematical …, 2023 - esaim-m2an.org
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 …
only locally Lipschitz continuous. We formulate an adaptive iterative linearized finite element …
[HTML][HTML] On the convergence of adaptive iterative linearized Galerkin methods
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 …
equations exists. In this work we will revisit a unified iteration scheme in Hilbert spaces from …
On full linear convergence and optimal complexity of adaptive FEM with inexact solver
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 …
compute an approximation of user-prescribed accuracy at quasi-minimal computational …
Guaranteed, locally efficient, and robust a posteriori estimates for nonlinear elliptic problems in iteration-dependent norms. An orthogonal decomposition result based …
K Mitra, M Vohralík - 2023 - inria.hal.science
We consider numerical approximations of nonlinear, monotone, and Lipschitz-continuous
elliptic problems, with gradient-dependent or gradient-independent diffusivity. For this …
elliptic problems, with gradient-dependent or gradient-independent diffusivity. For this …
Adaptive inexact smoothing Newton method for a nonconforming discretization of a variational inequality
IB Gharbia, J Ferzly, M Vohralík, S Yousef - Computers & Mathematics with …, 2023 - Elsevier
We develop in this work an adaptive inexact smoothing Newton method for a nonconforming
discretization of a variational inequality. As a model problem, we consider the contact …
discretization of a variational inequality. As a model problem, we consider the contact …
A numerical energy reduction approach for semilinear diffusion-reaction boundary value problems based on steady-state iterations
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 …
boundary value problems, where the nonlinear reaction terms need to be neither monotone …