A Posteriori Error Control in Adaptive Qualocation Boundary Element Analysis for a Logarithmic-Kernel Integral Equation of the First Kind. - Carsten Carstensen; Dirk Praetorius (SIAM J. Sci. Comput., 2003)

Residual-based a posteriori error estimate for hypersingular equation on surfaces. - Carsten Carstensen; Matthias Maischak; Dirk Praetorius; Ernst P. Stephan (Numerische Mathematik, 2004)

H-Matrix Techniques for Stray-Field Computations in Computational Micromagnetics. - Nikola Popovic; Dirk Praetorius (LSSC, 2005)

Applications of H -Matrix Techniques in Micromagnetics. - Nikola Popovic; Dirk Praetorius (Computing, 2005)

New a posteriori error estimates for singular boundary value problems. - Winfried Auzinger; Othmar Koch; Dirk Praetorius; Ewa Weinmüller (Numer. Algorithms, 2005)

Numerical Analysis for a Macroscopic Model in Micromagnetics. - Carsten Carstensen; Dirk Praetorius (SIAM J. Numer. Anal., 2005)

Averaging Techniques for the Effective Numerical Solution of Symm's Integral Equation of the First Kind. - Carsten Carstensen; Dirk Praetorius (SIAM J. Sci. Comput., 2006)

Averaging Techniques for the A Posteriori BEM Error Control for a Hypersingular Integral Equation in Two Dimensions. - Carsten Carstensen; Dirk Praetorius (SIAM J. Sci. Comput., 2007)

Simple a posteriori error estimators for the h-version of the boundary element method. - Samuel Ferraz-Leite; Dirk Praetorius (Computing, 2008)

A Posteriori Error Estimate and Adaptive Mesh Refinement for the Cell-Centered Finite Volume Method for Elliptic Boundary Value Problems. - Christoph Erath; Dirk Praetorius (SIAM J. Numer. Anal., 2008)

Collocation methods for index 1 DAEs with a singularity of the first kind. - Othmar Koch; Roswitha März; Dirk Praetorius; Ewa Weinmüller (Math. Comput., 2010)

Convergence of simple adaptive Galerkin schemes based on h - h/2 error estimators. - Samuel Ferraz-Leite; Christoph Ortner; Dirk Praetorius (Numerische Mathematik, 2010)

Efficient implementation of adaptive P1-FEM in Matlab. - Stefan A. Funken; Dirk Praetorius; Philipp Wissgott (Comput. Methods Appl. Math., 2011)

On the Convergence of Adaptive Nonconforming Finite Element Methods for a Class of Convex Variational Problems. - Christoph Ortner; Dirk Praetorius (SIAM J. Numer. Anal., 2011)

Stabilisation yields strong convergence of macroscopic magnetisation vectors for micromagnetics without exchange energy. - Carsten Carstensen; Dirk Praetorius (J. Num. Math., 2012)

Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics. - Samuel Ferraz-Leite; Jens Markus Melenk; Dirk Praetorius (Numerische Mathematik, 2012)

Efficiency and Optimality of Some Weighted-Residual Error Estimator for Adaptive 2D Boundary Element Methods. - Markus Aurada; Michael Feischl; Thomas Führer; Michael Karkulik; Dirk Praetorius (Comput. Methods Appl. Math., 2013)

Quasi-optimal Convergence Rate for an Adaptive Boundary Element Method. - Michael Feischl; Michael Karkulik; Jens Markus Melenk; Dirk Praetorius (SIAM J. Numer. Anal., 2013)

Spin-polarized transport in ferromagnetic multilayers: An unconditionally convergent FEM integrator. - Claas Abert; Gino Hrkac; Marcus Page; Dirk Praetorius; Michele Ruggeri; Dieter Suess (Comput. Math. Appl., 2014)

Axioms of adaptivity. - Carsten Carstensen; Michael Feischl; Marcus Page; Dirk Praetorius (Comput. Math. Appl., 2014)

Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor. - Michael Feischl; Thomas Führer; Gregor Mitscha-Eibl; Dirk Praetorius; Ernst P. Stephan (Comput. Methods Appl. Math., 2014)

Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data. - Michael Feischl; Marcus Page; Dirk Praetorius (J. Comput. Appl. Math., 2014)

HILBERT - a MATLAB implementation of adaptive 2D-BEM - HILBERT Is a Lovely Boundary Element Research Tool. - Markus Aurada; Michael Ebner; Michael Feischl; Samuel Ferraz-Leite; Thomas Führer; Petra Goldenits; Michael Karkulik; Markus Mayr; Dirk Praetorius (Numer. Algorithms, 2014)

Adaptive FEM with Optimal Convergence Rates for a Certain Class of Nonsymmetric and Possibly Nonlinear Problems. - Michael Feischl; Thomas Führer; Dirk Praetorius (SIAM J. Numer. Anal., 2014)

Optimal additive Schwarz methods for the hp-BEM: The hypersingular integral operator in 3D on locally refined meshes. - Thomas Führer; Jens Markus Melenk; Dirk Praetorius; Alexander Rieder (Comput. Math. Appl., 2015)

FEM-BEM coupling for the large-body limit in micromagnetics. - Markus Aurada; Jens Markus Melenk; Dirk Praetorius (J. Comput. Appl. Math., 2015)

ℋ-matrix approximability of the inverses of FEM matrices. - Markus Faustmann; Jens Markus Melenk; Dirk Praetorius (Numerische Mathematik, 2015)

Stability of symmetric and nonsymmetric FEM-BEM couplings for nonlinear elasticity problems. - Michael Feischl; Thomas Führer; Michael Karkulik; Dirk Praetorius (Numerische Mathematik, 2015)

Existence of ℋ-matrix approximants to the inverses of BEM matrices: The simple-layer operator. - Markus Faustmann; Jens Markus Melenk; Dirk Praetorius (Math. Comput., 2016)

Adaptive boundary element methods for optimal convergence of point errors. - Michael Feischl; Gregor Gantner; Alexander Haberl; Dirk Praetorius; Thomas Führer (Numerische Mathematik, 2016)

Adaptive Vertex-Centered Finite Volume Methods with Convergence Rates. - Christoph Erath; Dirk Praetorius (SIAM J. Numer. Anal., 2016)

An Abstract Analysis of Optimal Goal-Oriented Adaptivity. - Michael Feischl; Dirk Praetorius; Kristoffer G. van der Zee (SIAM J. Numer. Anal., 2016)

Local inverse estimates for non-local boundary integral operators. - Markus Aurada; Michael Feischl; Thomas Führer; Michael Karkulik; Jens Markus Melenk; Dirk Praetorius (Math. Comput., 2017)

Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations. - Michael Feischl; Gregor Gantner; Alexander Haberl; Dirk Praetorius (Numerische Mathematik, 2017)

A linear Uzawa-type FEM-BEM solver for nonlinear transmission problems. - Thomas Führer; Dirk Praetorius (Comput. Math. Appl., 2018)

Convergence of an implicit-explicit midpoint scheme for computational micromagnetics. - Dirk Praetorius; Michele Ruggeri; Bernhard Stiftner (Comput. Math. Appl., 2018)

Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics. - Gino Hrkac; Carl-Martin Pfeiler; Dirk Praetorius; Michele Ruggeri; Antonio Segatti; Bernhard Stiftner (Adv. Comput. Math., 2019)

Adaptive isogeometric boundary element methods with local smoothness control. - Gregor Gantner; Dirk Praetorius; Stefan Schimanko (CoRR, 2019)

The saturation assumption yields optimal convergence of two-level adaptive BEM. - Dirk Praetorius; Michele Ruggeri; Ernst P. Stephan (CoRR, 2019)

Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics. - Giovanni Di Fratta; Michael Innerberger; Dirk Praetorius (CoRR, 2019)

Adaptive boundary element methods for the computation of the electrostatic capacity on complex polyhedra. - Timo Betcke; Alexander Haberl; Dirk Praetorius (J. Comput. Phys., 2019)

Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics. - Johannes Kraus 001; Carl-Martin Pfeiler; Dirk Praetorius; Michele Ruggeri; Bernhard Stiftner (J. Comput. Phys., 2019)

Adaptive BEM with inexact PCG solver yields almost optimal computational costs. - Thomas Führer; Alexander Haberl; Dirk Praetorius; Stefan Schimanko (Numerische Mathematik, 2019)

Convergence of Adaptive Stochastic Galerkin FEM. - Alex Bespalov; Dirk Praetorius; Leonardo Rocchi; Michele Ruggeri (SIAM J. Numer. Anal., 2019)

Adaptive IGAFEM with optimal convergence rates: T-splines. - Gregor Gantner; Dirk Praetorius (Comput. Aided Geom. Des., 2020)

Optimal convergence behavior of adaptive FEM driven by simple (h-h∕2)-type error estimators. - Christoph Erath; Gregor Gantner; Dirk Praetorius (Comput. Math. Appl., 2020)

A short note on plain convergence of adaptive least-squares finite element methods. - Thomas Führer; Dirk Praetorius (Comput. Math. Appl., 2020)

Adaptive BEM for elliptic PDE systems, Part I: Abstract framework for weakly-singular integral equations. - Gregor Gantner; Dirk Praetorius (CoRR, 2020)

Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin FEM. - Alex Bespalov; Dirk Praetorius; Michele Ruggeri (CoRR, 2020)

A note on energy contraction and optimal convergence of adaptive iterative linearized finite element methods. - Pascal Heid; Dirk Praetorius; Thomas P. Wihler (CoRR, 2020)

Plain convergence of adaptive algorithms without exploiting reliability and efficiency. - Gregor Gantner; Dirk Praetorius (CoRR, 2020)

Micromagnetics of thin films in the presence of Dzyaloshinskii-Moriya interaction. - Elisa Davoli; Giovanni Di Fratta; Dirk Praetorius; Michele Ruggeri (CoRR, 2020)

Computational micromagnetics with Commics. - Carl-Martin Pfeiler; Michele Ruggeri; Bernhard Stiftner; Lukas Exl; Matthias Hochsteger; Gino Hrkac; Joachim Schöberl; Norbert J. Mauser; Dirk Praetorius (Comput. Phys. Commun., 2020)

Dörfler marking with minimal cardinality is a linear complexity problem. - Carl-Martin Pfeiler; Dirk Praetorius (Math. Comput., 2020)

Optimal Convergence Rates for Goal-Oriented FEM with Quadratic Goal Functional. - Roland Becker; Michael Innerberger; Dirk Praetorius (Comput. Methods Appl. Math., 2021)

Energy Contraction and Optimal Convergence of Adaptive Iterative Linearized Finite Element Methods. - Pascal Heid; Dirk Praetorius; Thomas P. Wihler (Comput. Methods Appl. Math., 2021)

Instance-Optimal Goal-Oriented Adaptivity. - Michael Innerberger; Dirk Praetorius (Comput. Methods Appl. Math., 2021)

Reliable Methods of Mathematical Modeling. - Dirk Praetorius; Sergey I. Repin; Stefan A. Sauter (Comput. Methods Appl. Math., 2021)

Accurate Benchmark Computations of the Polarizability Tensor for Characterising Small Conducting Inclusions. - A. A. S. Amad; Paul D. Ledger; Timo Betcke; Dirk Praetorius (CoRR, 2021)

Mathematical foundations of adaptive isogeometric analysis. - Annalisa Buffa; Gregor Gantner; Carlotta Giannelli; Dirk Praetorius; Rafael Vázquez Hernández (CoRR, 2021)

Unconditional well-posedness and IMEX improvement of a family of predictor-corrector methods in micromagnetics. - Norbert J. Mauser; Carl-Martin Pfeiler; Dirk Praetorius; Michele Ruggeri (CoRR, 2021)

Goal-oriented adaptive finite element method for semilinear elliptic PDEs. - Roland Becker; Maximilian Brunner; Michael Innerberger; Jens Markus Melenk; Dirk Praetorius (CoRR, 2021)

Two-Level a Posteriori Error Estimation for Adaptive Multilevel Stochastic Galerkin Finite Element Method. - Alex Bespalov; Dirk Praetorius; Michele Ruggeri (SIAM/ASA J. Uncertain. Quantification, 2021)

Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian. - Markus Faustmann; Jens Markus Melenk; Dirk Praetorius (Math. Comput., 2021)

Rate optimality of adaptive finite element methods with respect to overall computational costs. - Gregor Gantner; Alexander Haberl; Dirk Praetorius; Stefan Schimanko (Math. Comput., 2021)

Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver. - Alexander Haberl; Dirk Praetorius; Stefan Schimanko; Martin Vohralík (Numerische Mathematik, 2021)

Functional a posteriori error estimates for boundary element methods. - Stefan Kurz; Dirk Pauly; Dirk Praetorius; Sergey I. Repin; Daniel Sebastian (Numerische Mathematik, 2021)

Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs. - Roland Becker; Maximilian Brunner; Michael Innerberger; Jens Markus Melenk; Dirk Praetorius (Comput. Math. Appl., 2022)

Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations. - Gregor Gantner; Dirk Praetorius (Comput. Math. Appl., 2022)

Stable Implementation of Adaptive IGABEM in 2D in MATLAB. - Gregor Gantner; Dirk Praetorius; Stefan Schimanko (Comput. Methods Appl. Math., 2022)

MooAFEM: An object oriented Matlab code for higher-order (nonlinear) adaptive FEM. - Michael Innerberger; Dirk Praetorius (CoRR, 2022)

Goal-oriented adaptive multilevel stochastic Galerkin FEM. - Alex Bespalov; Dirk Praetorius; Michele Ruggeri (CoRR, 2022)

Optimal computational costs of AFEM with optimal local hp-robust multigrid solver. - Michael Innerberger; Ani Miraçi; Dirk Praetorius; Julian Streitberger (CoRR, 2022)

Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs. - Roland Becker; Maximilian Brunner; Michael Innerberger; Jens Markus Melenk; Dirk Praetorius (CoRR, 2022)

Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs. - Maximilian Brunner; Pascal Heid; Michael Innerberger; Ani Miraçi; Dirk Praetorius; Julian Streitberger (CoRR, 2022)

Adaptive FEM for Parameter-Errors in Elliptic Linear-Quadratic Parameter Estimation Problems. - Roland Becker; Michael Innerberger; Dirk Praetorius (SIAM J. Numer. Anal., 2022)

MooAFEM: An object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs. - Michael Innerberger; Dirk Praetorius (Appl. Math. Comput., 2023)

The Mass-Lumped Midpoint Scheme for Computational Micromagnetics: Newton Linearization and Application to Magnetic Skyrmion Dynamics. - Giovanni Di Fratta; Carl-Martin Pfeiler; Dirk Praetorius; Michele Ruggeri (Comput. Methods Appl. Math., 2023)

Goal-oriented adaptive finite element methods with optimal computational complexity. - Roland Becker; Gregor Gantner; Michael Innerberger; Dirk Praetorius (Numerische Mathematik, 2023)

Plain convergence of goal-oriented adaptive FEM. - Valentin Helml; Michael Innerberger; Dirk Praetorius (Comput. Math. Appl., 2023)

Parameter-robust full linear convergence and optimal complexity of adaptive iteratively linearized FEM for nonlinear PDEs. - Ani Miraçi; Dirk Praetorius; Julian Streitberger (CoRR, 2024)

Iterative solvers in adaptive FEM. - Philipp Bringmann; Ani Miraçi; Dirk Praetorius (CoRR, 2024)

Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 1). - Michael Feischl; Dirk Praetorius; Michele Ruggeri (Comput. Methods Appl. Math., 2024)

Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 2). - Michael Feischl; Dirk Praetorius; Michele Ruggeri (Comput. Methods Appl. Math., 2024)

On full linear convergence and optimal complexity of adaptive FEM with inexact solver. - Philipp Bringmann; Michael Feischl; Ani Miraçi; Dirk Praetorius; Julian Streitberger (Comput. Math. Appl., 2025)

Goal-Oriented Error Estimation and Adaptivity for Stochastic Collocation FEM. - Alex Bespalov; Dirk Praetorius; Thomas Round; Andrey Savinov (SIAM/ASA J. Uncertain. Quantification, 2025)

Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs. - Maximilian Brunner; Dirk Praetorius; Julian Streitberger (Numerische Mathematik, 2025)

Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs. - Philipp Bringmann; Maximilian Brunner; Dirk Praetorius; Julian Streitberger (J. Num. Math., 2025)

Convergence of adaptive boundary element methods driven by functional a posteriori error estimates. - Alexander Freiszlinger; Dirk Pauly; Dirk Praetorius (CoRR, 2025)