50 citations · 71 across the 21 of their papers we have counts for
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BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: IMEX time-stepping and full effective field
Michele Aldé, Dirk Praetorius, Agus L. Soenjaya
We extend the BDF2-type finite-element integrator proposed in [M. Aldé, M. Feischl, D. Praetorius; BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: unco…
Optimal convergence of adaptive BEM driven by functional-type error estimators
Maximilian Brunner, Alexander Freiszlinger, Dirk Pauly +1
In the present work, we derive functional upper bounds for the potential error arising from boundary element discretizations of the Laplace-Dirichlet problem. These bounds are base…
Optimal complexity of adaptive FEM for second-order linear elliptic PDEs driven by non-residual estimators, Part I: Symmetric PDEs
Philipp Bringmann, Aleksandar Dadic, Dario Ferloni +3
We consider adaptive finite element methods for symmetric second-order linear elliptic PDEs, where the adaptive algorithm steers the local mesh refinement as well as an iterative a…
Quasi-optimal complexity of iterative Galerkin methods driven by an elliptic reconstruction error estimator
Maximilian Brunner, Gregor Gantner, Christoph Lietz +1
We study an iterative Galerkin method for quasilinear elliptic problems in the Browder-Minty setting. The resulting discrete nonlinear systems are solved by linearization via a (da…
BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: a-priori error estimates
Michele Aldé, Dirk Praetorius, Michael Feischl
We consider the Landau-Lifshitz-Gilbert equation (LLG), which models time-dependent micromagnetic phenomena. We analyze a fully discrete scheme that combines first-order finite ele…
Adaptive finite element methods with optimally preconditioned GMRES guarantee optimal complexity
Thomas Führer, Paula Hilbert, Ani Miraçi +1
We analyze optimal complexity of adaptive finite element methods (AFEMs) for general second-order linear elliptic partial differential equations (PDEs) in the Lax-Milgram setting.…
Minimum residual discretization of a semilinear elliptic problem
Carlos García Vera, Norbert Heuer, Dirk Praetorius
We propose a least-squares penalization as a means to extend the discontinuous Petrov-Galerkin (DPG) method with optimal test functions to a class of semilinear elliptic problems.…
New a posteriori error estimates for full-space transmission problems
Alexander Freiszlinger, Dirk Pauly, Dirk Praetorius +1
In the present work, we derive functional upper bounds for the potential error arising from finite-element boundary-element coupling formulations for a nonlinear Poisson-type trans…
Multigoal-oriented adaptive finite element method with convergence rates
Roland Becker, Maximilian Brunner, Paula Hilbert +2
We formulate and analyze a goal-oriented adaptive finite element method for a symmetric linear elliptic partial differential equation (PDE) that can simultaneously deal with multip…
Unconditional full linear convergence and quasi-optimal complexity of smoothed adaptive finite element methods
Philipp Bringmann, Christoph Lietz, Dirk Praetorius
We present the first rigorous convergence analysis of the smoothed adaptive finite element method (S-AFEM) proposed in [Mulita, Giani, Heltai: SIAM J. Sci. Comput. 43, 2021]. S-AFE…
Generalized preconditioned conjugate gradients for adaptive FEM with optimal complexity
Paula Hilbert, Ani Miraçi, Dirk Praetorius
We consider adaptive finite element methods (AFEMs) with inexact algebraic solvers for second-order symmetric linear elliptic diffusion problems. Optimal complexity of AFEM, i.e.,…