Dirk Praetorius

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Jens Markus Melenk, Markus Faustmann, Dirk Praetorius, 2013, Numerische Mathematik.

Efficiency and Optimality of Some Weighted-Residual Error Estimator for Adaptive 2D Boundary Element Methods

Michael Karkulik, Michael Feischl, Dirk Praetorius, 2013, Comput. Methods Appl. Math..

Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data☆

Michael Feischl, Dirk Praetorius, Marcus Page, 2014, J. Comput. Appl. Math..

Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics

Dirk Praetorius, Johannes Kraus, Carl-Martin Pfeiler, 2018, J. Comput. Phys..

Quasi-optimal Convergence Rate for an Adaptive Boundary Element Method

Michael Karkulik, Jens Markus Melenk, Michael Feischl, 2013, SIAM J. Numer. Anal..

On the Convergence of Adaptive Nonconforming Finite Element Methods for a Class of Convex Variational Problems

Christoph Ortner, Dirk Praetorius, C. Ortner, 2011, SIAM J. Numer. Anal..

Adaptive Boundary Element Methods

Norbert Heuer, Michael Karkulik, Michael Feischl, 2014 .

Simple a posteriori error estimators for the h-version of the boundary element method

Dirk Praetorius, Samuel Ferraz-Leite, S. Ferraz-Leite, 2008, Computing.

New a posteriori error estimates for singular boundary value problems

Winfried Auzinger, Othmar Koch, Ewa Weinmüller, 2005, Numerical Algorithms.

Adaptive boundary element methods for the computation of the electrostatic capacity on complex polyhedra

Dirk Praetorius, Timo Betcke, Alexander Haberl, 2019, J. Comput. Phys..

Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor

Michael Feischl, Dirk Praetorius, Thomas Führer, 2014, Comput. Methods Appl. Math..

Instance-Optimal Goal-Oriented Adaptivity

Dirk Praetorius, Michael Innerberger, D. Praetorius, 2019, Comput. Methods Appl. Math..

Adaptive isogeometric boundary element methods with local smoothness control pdf

Dirk Praetorius, Gregor Gantner, Stefan Schimanko, 2019, Mathematical Models and Methods in Applied Sciences.

Averaging Techniques for the Effective Numerical Solution of Symm's Integral Equation of the First Kind

Carsten Carstensen, Dirk Praetorius, C. Carstensen, 2005, SIAM J. Sci. Comput..

Stability of symmetric and nonsymmetric FEM–BEM couplings for nonlinear elasticity problems

Michael Karkulik, Michael Feischl, Dirk Praetorius, 2012, Numerische Mathematik.

Numerical Analysis for a Macroscopic Model in Micromagnetics

Carsten Carstensen, Dirk Praetorius, C. Carstensen, 2004, SIAM J. Numer. Anal..

Adaptive boundary element methods for optimal convergence of point errors

Michael Feischl, Dirk Praetorius, Thomas Führer, 2016, Numerische Mathematik.

H-Matrix Techniques for Stray-Field Computations in Computational Micromagnetics

Dirk Praetorius, Nikola Popovic, N. Popović, 2005, LSSC.

HILBERT — a MATLAB implementation of adaptive 2D-BEM

Michael Karkulik, Michael Feischl, Dirk Praetorius, 2014, Numerical Algorithms.

Optimal convergence behavior of adaptive FEM driven by simple (h-h∕2)-type error estimators

Dirk Praetorius, Christoph Erath, Gregor Gantner, 2018, Comput. Math. Appl..

MATLAB 7: Eine Einführung

Stefan Katzenbeisser, Dirk Praetorius, Christoph Überhuber, 2006 .

Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian

Jens Markus Melenk, Markus Faustmann, Dirk Praetorius, 2019 .

A posteriori error estimators, adaptivity, convergence, and implementation

Norbert Heuer, Michael Karkulik, Michael Feischl, 2014 .

Micromagnetics of thin films in the presence of Dzyaloshinskii-Moriya interaction pdf

Dirk Praetorius, Michele Ruggeri, Elisa Davoli, 2020, Mathematical Models and Methods in Applied Sciences.

Collocation methods for index 1 DAEs with a singularity of the first kind

Othmar Koch, Ewa Weinmüller, Dirk Praetorius, 2010, Math. Comput..

Adaptive Vertex-Centered Finite Volume Methods with Convergence Rates

Dirk Praetorius, Christoph Erath, 2016, SIAM J. Numer. Anal..

The saturation assumption yields optimal convergence of two-level adaptive BEM pdf

Dirk Praetorius, Ernst P. Stephan, Michele Ruggeri, 2019, Applied Numerical Mathematics.

An Abstract Analysis of Optimal Goal-Oriented Adaptivity

Michael Feischl, Dirk Praetorius, Kristoffer G. van der Zee, 2015, SIAM J. Numer. Anal..

Computational micromagnetics with Commics

Dirk Praetorius, Joachim Schöberl, Matthias Hochsteger, 2018, Comput. Phys. Commun..

ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve☆

Michael Karkulik, Michael Feischl, Dirk Praetorius, 2013, Engineering analysis with boundary elements.

Convergence of Adaptive Stochastic Galerkin FEM

Dirk Praetorius, Michele Ruggeri, Leonardo Rocchi, 2018, SIAM J. Numer. Anal..

FEM–BEM coupling for the large-body limit in micromagnetics

Jens Markus Melenk, Dirk Praetorius, Markus Aurada, 2015, J. Comput. Appl. Math..

Efficient implementation of adaptive P1-FEM in Matlab

Stefan A. Funken, Dirk Praetorius, Philipp Wissgott, 2011, Comput. Methods Appl. Math..

Rate Optimality of Adaptive Algorithms

Carsten Carstensen, Michael Feischl, Dirk Praetorius, 2014 .

Existence of ℋ-matrix approximants to the inverses of BEM matrices: The simple-layer operator

Jens Markus Melenk, Markus Faustmann, Dirk Praetorius, 2013, Math. Comput..

A short note on plain convergence of adaptive least-squares finite element methods pdf

Dirk Praetorius, Thomas Führer, 2020, Comput. Math. Appl..

Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations

Michael Feischl, Dirk Praetorius, Gregor Gantner, 2015, Numerische Mathematik.

A linear Uzawa-type FEM-BEM solver for nonlinear transmission problems

Dirk Praetorius, Thomas Führer, T. Führer, 2017, Comput. Math. Appl..

Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs

Dirk Praetorius, Michele Ruggeri, Leonardo Rocchi, 2018, Computer Methods in Applied Mechanics and Engineering.

Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators

Christoph Ortner, Dirk Praetorius, Samuel Ferraz-Leite, 2010, Numerische Mathematik.

Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver pdf

Dirk Praetorius, Alexander Haberl, Stefan Schimanko, 2020, Numerische Mathematik.

Adaptive BEM with inexact PCG solver yields almost optimal computational costs

Dirk Praetorius, Thomas Führer, Alexander Haberl, 2018, Numerische Mathematik.

Rate optimality of adaptive finite element methods with respect to the overall computational costs pdf

Dirk Praetorius, Gregor Gantner, Alexander Haberl, 2020, Math. Comput..

Stabilisation yields strong convergence of macroscopic magnetisation vectors for micromagnetics without exchange energy

Carsten Carstensen, Dirk Praetorius, C. Carstensen, 2012, J. Num. Math..

Estimator Reduction and Convergence of Adaptive FEM and BEM

Dirk Praetorius, Markus Aurada, Samuel Ferraz-Leite, 2009 .

Spin-polarized transport in ferromagnetic multilayers: An unconditionally convergent FEM integrator

Dirk Praetorius, Claas Abert, Dieter Suess, 2014, Comput. Math. Appl..

Adaptive FEM with Optimal Convergence Rates for a Certain Class of Nonsymmetric and Possibly Nonlinear Problems

Michael Feischl, Dirk Praetorius, Thomas Führer, 2012, SIAM J. Numer. Anal..

Local inverse estimates for non-local boundary integral operators

Michael Karkulik, Jens Markus Melenk, Michael Feischl, 2015, Math. Comput..

Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics

Dirk Praetorius, Antonio Segatti, Carl-Martin Pfeiler, 2017, Adv. Comput. Math..

Applications of -Matrix Techniques in Micromagnetics

Dirk Praetorius, Nikola Popovic, N. Popović, 2005, Computing.

Residual-based a posteriori error estimate for hypersingular equation on surfaces

Carsten Carstensen, Dirk Praetorius, Ernst P. Stephan, 2004, Numerische Mathematik.

Hilbert (Release 2): A MATLAB Implementation of Adaptive BEM

Michael Karkulik, Michael Feischl, Dirk Praetorius, 2010 .

Optimal additive Schwarz methods for the hp-BEM: The hypersingular integral operator in 3D on locally refined meshes

Jens Markus Melenk, Dirk Praetorius, Thomas Führer, 2014, Comput. Math. Appl..

Adaptive BEM for elliptic PDE systems, part I: abstract framework, for weakly-singular integral equations pdf

Dirk Praetorius, Gregor Gantner, D. Praetorius, 2020, Applicable Analysis.

A Posteriori Error Estimate and Adaptive Mesh Refinement for the Cell-Centered Finite Volume Method for Elliptic Boundary Value Problems

Dirk Praetorius, Christoph Erath, D. Praetorius, 2008, SIAM J. Numer. Anal..

Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin FEM pdf

Dirk Praetorius, Michele Ruggeri, Alex Bespalov, 2020, ArXiv.

Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics pdf

Dirk Praetorius, Michael Innerberger, Giovanni Di Fratta, 2019, ArXiv.

Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations

Michael Feischl, Dirk Praetorius, Gregor Gantner, 2014, Computer methods in applied mechanics and engineering.

Adaptive IGAFEM with optimal convergence rates: T-splines

Dirk Praetorius, Gregor Gantner, 2020, Comput. Aided Geom. Des..

Functional a posteriori error estimates for boundary element methods pdf

Sergey Repin, Stefan Kurz, Dirk Praetorius, 2019, ArXiv.

Convergence of an implicit-explicit midpoint scheme for computational micromagnetics

Dirk Praetorius, Michele Ruggeri, Bernhard Stiftner, 2018, Comput. Math. Appl..

A note on energy contraction and optimal convergence of adaptive iterative linearized finite element methods pdf

Dirk Praetorius, Thomas P. Wihler, Pascal Heid, 2020, ArXiv.

A three-dimensional spin-diffusion model for micromagnetics

Christoph Vogler, Dirk Praetorius, Claas Abert, 2014, Scientific Reports.

A Non-Conforming Finite Element Method for Convex Variational Problems

Christoph Ortner, Dirk Praetorius, 2008 .

Adaptive Boundary Element Methods Based on Accurate a Posteriori Error Estimation

Dirk Praetorius, Samuel Ferraz-Leite, 2008 .

Axioms of adaptivity

Carsten Carstensen, Michael Feischl, Dirk Praetorius, 2013, Comput. Math. Appl..

Averaging Techniques for the A Posteriori BEM Error Control for a Hypersingular Integral Equation in Two Dimensions

Carsten Carstensen, Dirk Praetorius, C. Carstensen, 2007, SIAM J. Sci. Comput..

Optimal Convergence Rates for Goal-Oriented FEM with Quadratic Goal Functional pdf

Dirk Praetorius, Roland Becker, Michael Innerberger, 2020, Comput. Methods Appl. Math..

Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics

Dirk Praetorius, Samuel Ferraz-Leite, Jens Markus Melenk, 2012, Numerische Mathematik.

Convergence and rate optimality of adaptive multilevel stochastic Galerkin FEM

Dirk Praetorius, Michele Ruggeri, Alex Bespalov, 2021 .

Mathematical Foundations of Adaptive Isogeometric Analysis pdf

Carlotta Giannelli, Dirk Praetorius, Annalisa Buffa, 2021, Archives of Computational Methods in Engineering.

MATHICSE Technical Report : Mathematical Foundations of Adaptive Isogeometric Analysis

Carlotta Giannelli, Dirk Praetorius, Annalisa Buffa, 2021 .

Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations pdf

Dirk Praetorius, Gregor Gantner, 2021, ArXiv.

Two-Level a Posteriori Error Estimation for Adaptive Multilevel Stochastic Galerkin Finite Element Method

Dirk Praetorius, Michele Ruggeri, Alex Bespalov, 2021, SIAM/ASA J. Uncertain. Quantification.

Unconditional well-posedness and IMEX improvement of a family of predictor-corrector methods in micromagnetics pdf

Dirk Praetorius, Carl-Martin Pfeiler, Michele Ruggeri, 2021, Applied Numerical Mathematics.

Energy Contraction and Optimal Convergence of Adaptive Iterative Linearized Finite Element Methods

Dirk Praetorius, Thomas P. Wihler, Pascal Heid, 2021, Comput. Methods Appl. Math..

Reliable Methods of Mathematical Modeling

Sergey Repin, Dirk Praetorius, Stefan A. Sauter, 2021, Comput. Methods Appl. Math..

Adaptive FEM for parameter-errors in elliptic linear-quadratic parameter estimation problems pdf

Dirk Praetorius, Roland Becker, Michael Innerberger, 2021, ArXiv.

Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver pdf

Dirk Praetorius, Alexander Haberl, Stefan Schimanko, 2021, Numerische Mathematik.

Goal-oriented adaptive finite element method for semilinear elliptic PDEs pdf

Jens Markus Melenk, Dirk Praetorius, Roland Becker, 2021, ArXiv.

Goal-oriented adaptive finite element methods with optimal computational complexity pdf

Dirk Praetorius, Roland Becker, Gregor Gantner, 2021, ArXiv.

On 2D Newest Vertex Bisection: Optimality of Mesh-Closure and H1-Stability of L2-Projection

Michael Karkulik, Dirk Praetorius, M. Karkulik, 2013 .

Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements

Michael Feischl, Dirk Praetorius, Ernst P. Stephan, 2013, 1311.5782.

Existence of $\mathscr{H}$-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator

Jens Markus Melenk, Markus Faustmann, Dirk Praetorius, 2015, 1503.01943.

Energy norm based error estimators for adaptive BEM for hypersingular integral equations

Michael Karkulik, Michael Feischl, Dirk Praetorius, 2015 .

On the Convergence of Adaptive Non-Conforming Finite Element Methods

Christoph Ortner, Dirk Praetorius, 2008 .

Estimator reduction and convergence of adaptive BEM

Dirk Praetorius, Markus Aurada, Samuel Ferraz-Leite, 2012, Applied numerical mathematics : transactions of IMACS.

Convergence of adaptive FEM for elliptic obstacle problems

Michael Feischl, Dirk Praetorius, Marcus Page, 2011 .

MIXED CONFORMING ELEMENTS FOR THE LARGE-BODY LIMIT IN MICROMAGNETICS

Jens Markus Melenk, Dirk Praetorius, Markus Aurada, 2014 .

Optimal additive Schwarz methods for the h p -BEM

Jens Markus Melenk, Dirk Praetorius, Thomas Führer, 2015 .

Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines

Dirk Praetorius, Gregor Gantner, D. Praetorius, 2017, 1701.07764.

Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh‐refinement

Michael Karkulik, Dirk Praetorius, M. Karkulik, 2013 .

Multiscale modeling in micromagnetics: Existence of solutions and numerical integration

Michael Feischl, Dirk Praetorius, Florian Bruckner, 2012, 1209.5548.

A decoupled and unconditionally convergent linear FEM integrator for the Landau–Lifshitz–Gilbert equation with magnetostriction

Dirk Praetorius, Marcus Page, Ľubomír Baňas, 2014 .

A MATLAB IMPLEMENTATION OF ADAPTIVE BEM

Michael Karkulik, Michael Feischl, Dirk Praetorius, 2010 .

Convergent geometric integrator for the Landau‐Lifshitz‐Gilbert equation in micromagnetics

Dirk Praetorius, Dieter Suess, Petra Goldenits, 2011 .

HILBERT – A MATLAB Implementation of Adaptive BEM

Michael Karkulik, Dirk Praetorius, Michael Ebner, 2009 .

Simple error estimators for the Galerkin BEM for some hypersingular integral equation in 2D

Stefan A. Funken, Dirk Praetorius, Petra Goldenits, 2013 .

Convergence of adaptive boundary element methods

Carsten Carstensen, Dirk Praetorius, 2012 .

Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems

Michael Feischl, Dirk Praetorius, Markus Aurada, 2012 .

Quasi-optimal convergence rates for adaptive boundary element methods with data approximation, part I: weakly-singular integral equation

Michael Karkulik, Jens Markus Melenk, Michael Feischl, 2014 .

Inverse estimates for elliptic boundary integral operators and their application to the adaptive coupling of FEM and BEM

Michael Karkulik, Jens Markus Melenk, Michael Feischl, 2012, 1211.4360.

Remarks and examples concerning distance ellipsoids

Dirk Praetorius, D. Praetorius, 2002 .

Linear second-order IMEX-type integrator for the (eddy current) Landau–Lifshitz–Gilbert equation

Dirk Praetorius, Carl-Martin Pfeiler, Michele Ruggeri, 2017, 1711.10715.

Effective simulation of a macroscopic model for stationary micromagnetics

Carsten Carstensen, Dirk Praetorius, C. Carstensen, 2005 .

L2-orthogonal projections onto finite elements on locally refined meshes are H1-stable

Michael Karkulik, Dirk Praetorius, Carl-Martin Pfeiler, 2013, 1307.0917.

Multiscale Modeling in Micromagnetics: Well-Posedness and Numerical Integration

Michael Feischl, Dirk Praetorius, Florian Bruckner, 2012 .

Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data

Michael Feischl, Dirk Praetorius, Marcus Page, 2011 .

3D FEM-BEM-Coupling Method to solve Magnetostatic Maxwell Equations

Michael Feischl, Christoph Vogler, Dirk Praetorius, 2012 .

Residual A-Posteriori Error Estimates in BEM : Convergence of h-Adaptive Algorithms

Michael Karkulik, Jens Markus Melenk, Michael Feischl, 2011 .

Energy norm based a posteriori error estimation for boundary element methods in two dimensions

Stefan A. Funken, Dirk Praetorius, Samuel Ferraz-Leite, 2009 .

Adaptive FEM with inhomogeneous dirichlet data: Convergence and quasi-optimality in Rd

Michael Feischl, Dirk Praetorius, Markus Aurada, 2012 .

Adaptive BEM with optimal convergence rates for the Helmholtz equation

Dirk Praetorius, Timo Betcke, Alexander Haberl, 2018, Computer Methods in Applied Mechanics and Engineering.

Combining micromagnetism and magnetostatic Maxwell equations for multiscale magnetic simulations☆

Michael Feischl, Christoph Vogler, Dirk Praetorius, 2013, Journal of magnetism and magnetic materials.

Each H1/2–stable projection yields convergence and quasi–optimality of adaptive FEM with inhomogeneous Dirichlet data in Rd

Michael Feischl, Dirk Praetorius, Markus Aurada, 2013 .

On 2D newest vertex bisection: Optimality of mesh-closure and H 1 -stability of

Michael Karkulik, Dirk Praetorius, M. Karkulik, 2012 .

A self-consistent spin-diffusion model for micromagnetics

Christoph Vogler, Dirk Praetorius, Claas Abert, 2015, Scientific Reports.

Analysis of the Operator Δ^-1div Arising in Magnetic Models

Dirk Praetorius, D. Praetorius, 2004 .

An Effective Integrator for the Landau-Lifshitz-Gilbert Equation

Dirk Praetorius, Petra Goldenits, Gino Hrkac, 2012 .

Adaptive 2D IGA boundary element methods

Michael Feischl, Dirk Praetorius, Gregor Gantner, 2015, 1504.06164.

A New Proof for Existence of H -Matrix Approximants to the Inverse of FEM Matrices: The Dirichlet Problem for the Laplacian

Jens Markus Melenk, Markus Faustmann, Dirk Praetorius, 2014 .

Averaging Techniques for a Posteriori Error Control in Finite Element and Boundary Element Analysis

Carsten Carstensen, Dirk Praetorius, C. Carstensen, 2007 .

Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations

Michael Feischl, Dirk Praetorius, Thomas Führer, 2017 .

Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity

Michael Karkulik, Jens Markus Melenk, Michael Feischl, 2012, 1211.4225.

Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems

Dirk Praetorius, Alexander Haberl, Alex Bespalov, 2016, 1606.08319.

ASC Report No . 40 / 2009 Convergence of Data Perturbed Adaptive Boundary Element Methods

Dirk Praetorius, Markus Aurada, Petra Goldenits, 2009 .

Rate optimal adaptive FEM with inexact solver for nonlinear operators

Dirk Praetorius, Bernhard Stiftner, Gregor Gantner, 2016, 1611.05212.