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.,…
Newton's method in adaptive iteratively linearized FEM
Philipp Bringmann, Maximilian Brunner, Dirk Praetorius
This paper concerns the inclusion of Newton's method into an adaptive finite element method (FEM) for the solution of nonlinear partial differential equations (PDEs). It features a…
Energy minimization for skyrmions on planar thin films
Giovanni Di Fratta, Michael Innerberger, Dirk Praetorius +1
We consider an energy functional that arises in micromagnetic and liquid crystal theory on thin films. In particular, our energy comprises a non-convex term that models anti-symmet…
Global convergence of adaptive least-squares finite element methods for nonlinear PDEs
Philipp Bringmann, Dirk Praetorius
The Zarantonello fixed-point iteration is an established linearization scheme for quasilinear PDEs with strongly monotone and Lipschitz continuous nonlinearity in Hilbert spaces. T…
Convergence of adaptive boundary element methods driven by functional a posteriori error estimates
Alexander Freiszlinger, Dirk Pauly, Dirk Praetorius
The recent work [Kurz et al., Numer. Math., 147 (2021)] proposed functional a posteriori error estimates for boundary element methods (BEMs) together with a related adaptive mesh-r…
Goal-Oriented Error Estimation and Adaptivity for Stochastic Collocation FEM
Alex Bespalov, Dirk Praetorius, Thomas Round +1
We propose and analyze a general goal-oriented adaptive strategy for approximating quantities of interest (QoIs) associated with solutions to linear elliptic partial differential e…
Iterative solvers in adaptive FEM
Philipp Bringmann, Ani Miraçi, Dirk Praetorius
This chapter provides an overview of state-of-the-art adaptive finite element methods (AFEMs) for the numerical solution of second-order elliptic partial differential equations (PD…
Unconditional full linear convergence and optimal complexity of adaptive iteratively linearized FEM for nonlinear PDEs
Ani Miraçi, Dirk Praetorius, Julian Streitberger
We propose an adaptive iteratively linearized finite element method (AILFEM) in the context of strongly monotone nonlinear operators in Hilbert spaces. The approach combines adapti…
Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs
Maximilian Brunner, Dirk Praetorius, Julian Streitberger
We consider scalar semilinear elliptic PDEs, where the nonlinearity is strongly monotone, but only locally Lipschitz continuous. To linearize the arising discrete nonlinear problem…
Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs
Philipp Bringmann, Maximilian Brunner, Dirk Praetorius +1
We analyze a goal-oriented adaptive algorithm that aims to efficiently compute the quantity of interest with a linear goal functional and the solution to…
On full linear convergence and optimal complexity of adaptive FEM with inexact solver
Philipp Bringmann, Michael Feischl, Ani Miraci +2
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 time.…
Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems
Alex Bespalov, Alexander Haberl, Dirk Praetorius
We prove that for compactly perturbed elliptic problems, where the corresponding bilinear form satisfies a Garding inequality, adaptive mesh-refinement is capable of overcoming the…
Simultaneous quasi-optimal convergence in FEM-BEM coupling
Jens Markus Melenk, Dirk Praetorius, Barbara Wohlmuth
We consider the symmetric FEM-BEM coupling that connects two linear elliptic second order partial differential equations posed in a bounded domain and its complement, where the…