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12/01/2022
Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs
We consider a general nonsymmetric second-order linear elliptic PDE in t...
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11/08/2022
Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs
We consider scalar semilinear elliptic PDEs where the nonlinearity is st...
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10/19/2022
Optimal computational costs of AFEM with optimal local hp-robust multigrid solver
In this work, an adaptive finite element algorithm for symmetric second-...
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08/22/2022
Plain convergence of goal-oriented adaptive FEM
We discuss goal-oriented adaptivity in the frame of conforming finite el...
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08/19/2022
Goal-oriented adaptive multilevel stochastic Galerkin FEM
This paper is concerned with the numerical approximation of quantities o...
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03/12/2022
The mass-lumped midpoint scheme for computational micromagnetics: Newton linearization and application to magnetic skyrmion dynamics
We discuss a mass-lumped midpoint scheme for the numerical approximation...
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03/03/2022
MooAFEM: An object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs
We present an easily accessible, object oriented code (written exclusive...
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03/01/2022
Stable implementation of adaptive IGABEM in 2D in MATLAB
We report on our MATLAB program package IGABEM2D, which provides an easi...
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12/13/2021
Goal-oriented adaptive finite element method for semilinear elliptic PDEs
We formulate and analyze a goal-oriented adaptive finite element method ...
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12/01/2021
Unconditional well-posedness and IMEX improvement of a family of predictor-corrector methods in micromagnetics
Recently, Kim Wilkening (Convergence of a mass-lumped finite element...
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11/05/2021
Adaptive FEM for parameter-errors in elliptic linear-quadratic parameter estimation problems
We consider an elliptic linear-quadratic parameter estimation problem wi...
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07/14/2021
Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations
We formulate and analyze an adaptive algorithm for isogeometric analysis...
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07/05/2021
Mathematical foundations of adaptive isogeometric analysis
This paper reviews the state of the art and discusses recent development...
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01/27/2021
Goal-oriented adaptive finite element methods with optimal computational complexity
We consider a linear symmetric and elliptic PDE and a linear goal functi...
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10/29/2020
Micromagnetics of thin films in the presence of Dzyaloshinskii-Moriya interaction
In this paper, we study the thin-film limit of the micromagnetic energy ...
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09/02/2020
Plain convergence of adaptive algorithms without exploiting reliability and efficiency
We consider h-adaptive algorithms in the context of the finite element m...
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07/21/2020
A note on energy contraction and optimal convergence of adaptive iterative linearized finite element methods
In this note, we revisit a unified methodology for the iterative solutio...
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06/03/2020
Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin FEM
The paper considers a class of parametric elliptic partial differential ...
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05/22/2020
A short note on plain convergence of adaptive least-squares finite element methods
We show that adaptive least-squares finite element methods driven by the...
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04/27/2020
Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver
We consider a second-order elliptic boundary value problem with strongly...
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04/16/2020
Adaptive BEM for elliptic PDE systems, Part I: Abstract framework for weakly-singular integral equations
In the present work, we consider weakly-singular integral equations aris...
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03/30/2020
Optimal convergence rates for goal-oriented FEM with quadratic goal functional
We consider a linear elliptic PDE and a quadratic goal functional. The g...
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03/24/2020
Rate optimality of adaptive finite element methods with respect to the overall computational costs
We consider adaptive finite element methods for second-order elliptic PD...
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12/12/2019
Functional a posteriori error estimates for boundary element methods
Functional error estimates are well-estabilished tools for a posteriori ...
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10/10/2019
Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics
We consider the time-dependent Landau-Lifshitz-Gilbert equation. We prov...
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10/03/2019
Adaptive IGAFEM with optimal convergence rates: T-splines
We consider an adaptive algorithm for finite element methods for the iso...
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07/30/2019
Dörfler marking with minimal cardinality is a linear complexity problem
Most adaptive finite element strategies employ the Dörfler marking strat...
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07/30/2019
Instance-optimal goal-oriented adaptivity
We consider an adaptive finite element method with arbitrary but fixed p...
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07/15/2019
The saturation assumption yields optimal convergence of two-level adaptive BEM
We consider the convergence of adaptive BEM for weakly-singular and hype...
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03/05/2019