Relaxed Kačanov Scheme for the -Laplacian with Large Exponent
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 …
to the-Laplace problem with. The iterative scheme is easy to implement since each iterate …
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 …
Adaptive regularization, discretization, and linearization for nonsmooth problems based on primal–dual gap estimators
F Févotte, A Rappaport, M Vohralík - Computer Methods in Applied …, 2024 - Elsevier
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 …
energy functional. We adaptively regularize the nonsmooth nonlinearity so as to be able to …
Dörfler marking with minimal cardinality is a linear complexity problem
CM Pfeiler, D Praetorius - Mathematics of Computation, 2020 - ams.org
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 …
certain elements $\mathcal {M}\subseteq\mathcal {T} $ of a triangulation $\mathcal {T} $ for …
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 …
Goal-oriented mesh adaptation method for nonlinear problems including algebraic errors
V Dolejší, O Bartoš, F Roskovec - Computers & Mathematics with …, 2021 - Elsevier
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 …
differential equations. The setting of the adjoint problem and the resulting estimates are not …
[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 …
Adaptive iterative linearization Galerkin methods for nonlinear problems
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 …
Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative local …
[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 …