[HTML][HTML] Mathematical foundations of adaptive isogeometric analysis
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 …
adaptive isogeometric analysis, with special focus on the mathematical theory. This includes …
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 …
hp-robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs
M Innerberger, A Miraçi, D Praetorius… - ESAIM: Mathematical …, 2024 - esaim-m2an.org
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 …
of the discrete systems arising from the finite element discretization of symmetric second …
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] Review and computational comparison of adaptive least-squares finite element schemes
P Bringmann - Computers & Mathematics with Applications, 2024 - Elsevier
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 …
mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori …
[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 …
Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs
M Brunner, M Innerberger, A Miraçi… - IMA Journal of …, 2024 - academic.oup.com
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 …
in the framework of the Lax–Milgram lemma. We formulate and analyze an adaptive finite …
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 …