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ORCIDDirk Praetorius
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- affiliation: TU Wien, Vienna, Austria
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2020 – today
- 2025
[j65]Philipp Bringmann
, Michael Feischl, Ani Miraçi, Dirk Praetorius, Julian Streitberger:
On full linear convergence and optimal complexity of adaptive FEM with inexact solver. Comput. Math. Appl. 180: 102-129 (2025)- 2024
- [j64]Michael Feischl, Dirk Praetorius, Michele Ruggeri:
Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 1). Comput. Methods Appl. Math. 24(2): 279-282 (2024) - [j63]Michael Feischl, Dirk Praetorius, Michele Ruggeri:
Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 2). Comput. Methods Appl. Math. 24(3): 529-532 (2024) - [i37]Maximilian Brunner, Dirk Praetorius, Julian Streitberger:
Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs. CoRR abs/2401.06486 (2024) - [i36]Ani Miraçi, Dirk Praetorius, Julian Streitberger:
Parameter-robust full linear convergence and optimal complexity of adaptive iteratively linearized FEM for nonlinear PDEs. CoRR abs/2401.17778 (2024) - [i35]Philipp Bringmann, Ani Miraçi, Dirk Praetorius:
Iterative solvers in adaptive FEM. CoRR abs/2404.07126 (2024) - [i34]Alex Bespalov, Dirk Praetorius, Thomas Round, Andrey Savinov:
Goal-Oriented Error Estimation and Adaptivity for Stochastic Collocation FEM. CoRR abs/2406.05028 (2024) - 2023
- [j62]Michael Innerberger, Dirk Praetorius:
MooAFEM: An object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs. Appl. Math. Comput. 442: 127731 (2023) - [j61]Valentin Helml, Michael Innerberger, Dirk Praetorius:
Plain convergence of goal-oriented adaptive FEM. Comput. Math. Appl. 147: 130-149 (2023) - [j60]Giovanni Di Fratta, Carl-Martin Pfeiler, Dirk Praetorius, Michele Ruggeri:
The Mass-Lumped Midpoint Scheme for Computational Micromagnetics: Newton Linearization and Application to Magnetic Skyrmion Dynamics. Comput. Methods Appl. Math. 23(1): 145-175 (2023) - [j59]Roland Becker, Gregor Gantner, Michael Innerberger, Dirk Praetorius:
Goal-oriented adaptive finite element methods with optimal computational complexity. Numerische Mathematik 153(1): 111-140 (2023) - [i33]Philipp Bringmann, Michael Feischl, Ani Miraçi, Dirk Praetorius, Julian Streitberger:
On full linear convergence and optimal complexity of adaptive FEM with inexact solver. CoRR abs/2311.15738 (2023) - [i32]Philipp Bringmann, Maximilian Brunner, Dirk Praetorius, Julian Streitberger:
Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs. CoRR abs/2312.00489 (2023) - 2022
- [j58]Gregor Gantner, Dirk Praetorius:
Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations. Comput. Math. Appl. 117: 74-96 (2022) - [j57]Roland Becker, Maximilian Brunner, Michael Innerberger, Jens Markus Melenk, Dirk Praetorius:
Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs. Comput. Math. Appl. 118: 18-35 (2022) - [j56]Gregor Gantner, Dirk Praetorius, Stefan Schimanko:
Stable Implementation of Adaptive IGABEM in 2D in MATLAB. Comput. Methods Appl. Math. 22(3): 563-590 (2022) - [j55]Roland Becker, Michael Innerberger, Dirk Praetorius:
Adaptive FEM for Parameter-Errors in Elliptic Linear-Quadratic Parameter Estimation Problems. SIAM J. Numer. Anal. 60(3): 1450-1471 (2022) - [i31]Gregor Gantner, Dirk Praetorius, Stefan Schimanko:
Stable implementation of adaptive IGABEM in 2D in MATLAB. CoRR abs/2203.00394 (2022) - [i30]Michael Innerberger, Dirk Praetorius:
MooAFEM: An object oriented Matlab code for higher-order (nonlinear) adaptive FEM. CoRR abs/2203.01845 (2022) - [i29]Giovanni Di Fratta, Carl-Martin Pfeiler, Dirk Praetorius, Michele Ruggeri:
The mass-lumped midpoint scheme for computational micromagnetics: Newton linearization and application to magnetic skyrmion dynamics. CoRR abs/2203.06445 (2022) - [i28]Alex Bespalov, Dirk Praetorius, Michele Ruggeri:
Goal-oriented adaptive multilevel stochastic Galerkin FEM. CoRR abs/2208.09388 (2022) - [i27]Valentin Helml, Michael Innerberger, Dirk Praetorius:
Plain convergence of goal-oriented adaptive FEM. CoRR abs/2208.10143 (2022) - [i26]Michael Innerberger, Ani Miraçi, Dirk Praetorius, Julian Streitberger:
Optimal computational costs of AFEM with optimal local hp-robust multigrid solver. CoRR abs/2210.10415 (2022) - [i25]Roland Becker, Maximilian Brunner, Michael Innerberger, Jens Markus Melenk, Dirk Praetorius:
Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs. CoRR abs/2211.04123 (2022) - [i24]Maximilian Brunner, Pascal Heid, Michael Innerberger, Ani Miraçi, Dirk Praetorius, Julian Streitberger:
Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs. CoRR abs/2212.00353 (2022) - 2021
- [j54]Michael Innerberger, Dirk Praetorius:
Instance-Optimal Goal-Oriented Adaptivity. Comput. Methods Appl. Math. 21(1): 109-126 (2021) - [j53]Dirk Praetorius, Sergey I. Repin, Stefan A. Sauter:
Reliable Methods of Mathematical Modeling. Comput. Methods Appl. Math. 21(2): 263-266 (2021) - [j52]Roland Becker, Michael Innerberger, Dirk Praetorius:
Optimal Convergence Rates for Goal-Oriented FEM with Quadratic Goal Functional. Comput. Methods Appl. Math. 21(2): 267-288 (2021) - [j51]Pascal Heid, Dirk Praetorius, Thomas P. Wihler:
Energy Contraction and Optimal Convergence of Adaptive Iterative Linearized Finite Element Methods. Comput. Methods Appl. Math. 21(2): 407-422 (2021) - [j50]Alex Bespalov, Dirk Praetorius, Michele Ruggeri:
Two-Level a Posteriori Error Estimation for Adaptive Multilevel Stochastic Galerkin Finite Element Method. SIAM/ASA J. Uncertain. Quantification 9(3): 1184-1216 (2021) - [j49]Markus Faustmann, Jens Markus Melenk, Dirk Praetorius:
Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian. Math. Comput. 90(330): 1557-1587 (2021) - [j48]Gregor Gantner, Alexander Haberl, Dirk Praetorius, Stefan Schimanko:
Rate optimality of adaptive finite element methods with respect to overall computational costs. Math. Comput. 90(331): 2011-2040 (2021) - [j47]Alexander Haberl, Dirk Praetorius, Stefan Schimanko, Martin Vohralík:
Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver. Numerische Mathematik 147(3): 679-725 (2021) - [j46]Stefan Kurz, Dirk Pauly, Dirk Praetorius, Sergey I. Repin, Daniel Sebastian:
Functional a posteriori error estimates for boundary element methods. Numerische Mathematik 147(4): 937-966 (2021) - [i23]Roland Becker, Gregor Gantner, Michael Innerberger, Dirk Praetorius:
Goal-oriented adaptive finite element methods with optimal computational complexity. CoRR abs/2101.11407 (2021) - [i22]A. A. S. Amad, Paul D. Ledger, Timo Betcke, Dirk Praetorius:
Accurate Benchmark Computations of the Polarizability Tensor for Characterising Small Conducting Inclusions. CoRR abs/2106.15157 (2021) - [i21]Annalisa Buffa, Gregor Gantner, Carlotta Giannelli, Dirk Praetorius, Rafael Vázquez Hernández:
Mathematical foundations of adaptive isogeometric analysis. CoRR abs/2107.02023 (2021) - [i20]Gregor Gantner, Dirk Praetorius:
Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations. CoRR abs/2107.06613 (2021) - [i19]Roland Becker, Michael Innerberger, Dirk Praetorius:
Adaptive FEM for parameter-errors in elliptic linear-quadratic parameter estimation problems. CoRR abs/2111.03627 (2021) - [i18]Norbert J. Mauser, Carl-Martin Pfeiler, Dirk Praetorius, Michele Ruggeri:
Unconditional well-posedness and IMEX improvement of a family of predictor-corrector methods in micromagnetics. CoRR abs/2112.00451 (2021) - [i17]Roland Becker, Maximilian Brunner, Michael Innerberger, Jens Markus Melenk, Dirk Praetorius:
Goal-oriented adaptive finite element method for semilinear elliptic PDEs. CoRR abs/2112.06687 (2021) - 2020
- [j45]Gregor Gantner, Dirk Praetorius:
Adaptive IGAFEM with optimal convergence rates: T-splines. Comput. Aided Geom. Des. 81: 101906 (2020) - [j44]Christoph Erath, Gregor Gantner, Dirk Praetorius:
Optimal convergence behavior of adaptive FEM driven by simple (h-h∕2)-type error estimators. Comput. Math. Appl. 79(3): 623-642 (2020) - [j43]Thomas Führer, Dirk Praetorius:
A short note on plain convergence of adaptive least-squares finite element methods. Comput. Math. Appl. 80(6): 1619-1632 (2020) - [j42]Carl-Martin Pfeiler, Michele Ruggeri, Bernhard Stiftner, Lukas Exl, Matthias Hochsteger, Gino Hrkac, Joachim Schöberl, Norbert J. Mauser, Dirk Praetorius:
Computational micromagnetics with Commics. Comput. Phys. Commun. 248: 106965 (2020) - [j41]Carl-Martin Pfeiler, Dirk Praetorius:
Dörfler marking with minimal cardinality is a linear complexity problem. Math. Comput. 89(326): 2735-2752 (2020) - [i16]Gregor Gantner, Alexander Haberl, Dirk Praetorius, Stefan Schimanko:
Rate optimality of adaptive finite element methods with respect to the overall computational costs. CoRR abs/2003.10785 (2020) - [i15]Roland Becker, Michael Innerberger, Dirk Praetorius:
Optimal convergence rates for goal-oriented FEM with quadratic goal functional. CoRR abs/2003.13270 (2020) - [i14]Gregor Gantner, Dirk Praetorius:
Adaptive BEM for elliptic PDE systems, Part I: Abstract framework for weakly-singular integral equations. CoRR abs/2004.07762 (2020) - [i13]Alexander Haberl, Dirk Praetorius, Stefan Schimanko, Martin Vohralík:
Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver. CoRR abs/2004.13137 (2020) - [i12]Thomas Führer, Dirk Praetorius:
A short note on plain convergence of adaptive least-squares finite element methods. CoRR abs/2005.11015 (2020) - [i11]Alex Bespalov, Dirk Praetorius, Michele Ruggeri:
Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin FEM. CoRR abs/2006.02255 (2020) - [i10]Pascal Heid, Dirk Praetorius, Thomas P. Wihler:
A note on energy contraction and optimal convergence of adaptive iterative linearized finite element methods. CoRR abs/2007.10750 (2020) - [i9]Gregor Gantner, Dirk Praetorius:
Plain convergence of adaptive algorithms without exploiting reliability and efficiency. CoRR abs/2009.01349 (2020) - [i8]Elisa Davoli, Giovanni Di Fratta, Dirk Praetorius, Michele Ruggeri:
Micromagnetics of thin films in the presence of Dzyaloshinskii-Moriya interaction. CoRR abs/2010.15541 (2020)
2010 – 2019
- 2019
- [j40]Gino Hrkac, Carl-Martin Pfeiler, Dirk Praetorius, Michele Ruggeri, Antonio Segatti, Bernhard Stiftner:
Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics. Adv. Comput. Math. 45(3): 1329-1368 (2019) - [j39]Timo Betcke, Alexander Haberl, Dirk Praetorius:
Adaptive boundary element methods for the computation of the electrostatic capacity on complex polyhedra. J. Comput. Phys. 397 (2019) - [j38]Johannes Kraus, Carl-Martin Pfeiler, Dirk Praetorius, Michele Ruggeri, Bernhard Stiftner:
Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics. J. Comput. Phys. 398 (2019) - [j37]Thomas Führer, Alexander Haberl, Dirk Praetorius, Stefan Schimanko:
Adaptive BEM with inexact PCG solver yields almost optimal computational costs. Numerische Mathematik 141(4): 967-1008 (2019) - [j36]Alex Bespalov, Dirk Praetorius, Leonardo Rocchi, Michele Ruggeri:
Convergence of Adaptive Stochastic Galerkin FEM. SIAM J. Numer. Anal. 57(5): 2359-2382 (2019) - [i7]Gregor Gantner, Dirk Praetorius, Stefan Schimanko:
Adaptive isogeometric boundary element methods with local smoothness control. CoRR abs/1903.01830 (2019) - [i6]Dirk Praetorius, Michele Ruggeri, Ernst P. Stephan:
The saturation assumption yields optimal convergence of two-level adaptive BEM. CoRR abs/1907.06612 (2019) - [i5]Michael Innerberger, Dirk Praetorius:
Instance-optimal goal-oriented adaptivity. CoRR abs/1907.13035 (2019) - [i4]Carl-Martin Pfeiler, Dirk Praetorius:
Dörfler marking with minimal cardinality is a linear complexity problem. CoRR abs/1907.13078 (2019) - [i3]Gregor Gantner, Dirk Praetorius:
Adaptive IGAFEM with optimal convergence rates: T-splines. CoRR abs/1910.01311 (2019) - [i2]Giovanni Di Fratta, Michael Innerberger, Dirk Praetorius:
Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics. CoRR abs/1910.04630 (2019) - [i1]Stefan Kurz, Dirk Pauly, Dirk Praetorius, Sergey I. Repin, Daniel Sebastian:
Functional a posteriori error estimates for boundary element methods. CoRR abs/1912.05789 (2019) - 2018
- [j35]Dirk Praetorius, Michele Ruggeri, Bernhard Stiftner:
Convergence of an implicit-explicit midpoint scheme for computational micromagnetics. Comput. Math. Appl. 75(5): 1719-1738 (2018) - [j34]Thomas Führer, Dirk Praetorius:
A linear Uzawa-type FEM-BEM solver for nonlinear transmission problems. Comput. Math. Appl. 75(8): 2678-2697 (2018) - 2017
- [j33]Markus Aurada, Michael Feischl, Thomas Führer, Michael Karkulik, Jens Markus Melenk, Dirk Praetorius:
Local inverse estimates for non-local boundary integral operators. Math. Comput. 86(308): 2651-2686 (2017) - [j32]Michael Feischl, Gregor Gantner, Alexander Haberl, Dirk Praetorius:
Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations. Numerische Mathematik 136(1): 147-182 (2017) - 2016
- [j31]Markus Faustmann, Jens Markus Melenk, Dirk Praetorius:
Existence of ℋ-matrix approximants to the inverses of BEM matrices: The simple-layer operator. Math. Comput. 85(297): 119-152 (2016) - [j30]Michael Feischl, Gregor Gantner, Alexander Haberl, Dirk Praetorius, Thomas Führer:
Adaptive boundary element methods for optimal convergence of point errors. Numerische Mathematik 132(3): 541-567 (2016) - [j29]Michael Feischl, Dirk Praetorius, Kristoffer G. van der Zee:
An Abstract Analysis of Optimal Goal-Oriented Adaptivity. SIAM J. Numer. Anal. 54(3): 1423-1448 (2016) - [j28]Christoph Erath, Dirk Praetorius:
Adaptive Vertex-Centered Finite Volume Methods with Convergence Rates. SIAM J. Numer. Anal. 54(4): 2228-2255 (2016) - 2015
- [j27]Thomas Führer, Jens Markus Melenk, Dirk Praetorius, Alexander Rieder:
Optimal additive Schwarz methods for the hp-BEM: The hypersingular integral operator in 3D on locally refined meshes. Comput. Math. Appl. 70(7): 1583-1605 (2015) - [j26]Markus Aurada, Jens Markus Melenk, Dirk Praetorius:
FEM-BEM coupling for the large-body limit in micromagnetics. J. Comput. Appl. Math. 281: 10-31 (2015) - [j25]Michael Feischl, Thomas Führer, Michael Karkulik, Dirk Praetorius:
Stability of symmetric and nonsymmetric FEM-BEM couplings for nonlinear elasticity problems. Numerische Mathematik 130(2): 199-223 (2015) - [j24]Markus Faustmann, Jens Markus Melenk, Dirk Praetorius:
ℋ-matrix approximability of the inverses of FEM matrices. Numerische Mathematik 131(4): 615-642 (2015) - 2014
- [j23]Carsten Carstensen, Michael Feischl, Marcus Page, Dirk Praetorius:
Axioms of adaptivity. Comput. Math. Appl. 67(6): 1195-1253 (2014) - [j22]Claas Abert, Gino Hrkac, Marcus Page, Dirk Praetorius, Michele Ruggeri, Dieter Suess:
Spin-polarized transport in ferromagnetic multilayers: An unconditionally convergent FEM integrator. Comput. Math. Appl. 68(6): 639-654 (2014) - [j21]Michael Feischl, Thomas Führer, Gregor Mitscha-Eibl, Dirk Praetorius, Ernst P. Stephan:
Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor. Comput. Methods Appl. Math. 14(4): 485-508 (2014) - [j20]Michael Feischl, Marcus Page, Dirk Praetorius:
Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data. J. Comput. Appl. Math. 255: 481-501 (2014) - [j19]Markus Aurada, Michael Ebner, Michael Feischl, Samuel Ferraz-Leite, Thomas Führer, Petra Goldenits, Michael Karkulik, Markus Mayr, Dirk Praetorius:
HILBERT - a MATLAB implementation of adaptive 2D-BEM - HILBERT Is a Lovely Boundary Element Research Tool. Numer. Algorithms 67(1): 1-32 (2014) - [j18]Michael Feischl, Thomas Führer, Dirk Praetorius:
Adaptive FEM with Optimal Convergence Rates for a Certain Class of Nonsymmetric and Possibly Nonlinear Problems. SIAM J. Numer. Anal. 52(2): 601-625 (2014) - 2013
- [j17]Markus Aurada, Michael Feischl, Thomas Führer, Michael Karkulik, Dirk Praetorius:
Efficiency and Optimality of Some Weighted-Residual Error Estimator for Adaptive 2D Boundary Element Methods. Comput. Methods Appl. Math. 13(3): 305-332 (2013) - [j16]Michael Feischl, Michael Karkulik, Jens Markus Melenk, Dirk Praetorius:
Quasi-optimal Convergence Rate for an Adaptive Boundary Element Method. SIAM J. Numer. Anal. 51(2): 1327-1348 (2013) - 2012
- [j15]Carsten Carstensen, Dirk Praetorius:
Stabilisation yields strong convergence of macroscopic magnetisation vectors for micromagnetics without exchange energy. J. Num. Math. 20(2): 81-110 (2012) - [j14]Samuel Ferraz-Leite, Jens Markus Melenk, Dirk Praetorius:
Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics. Numerische Mathematik 122(1): 101-131 (2012) - 2011
- [j13]Stefan A. Funken, Dirk Praetorius, Philipp Wissgott:
Efficient implementation of adaptive P1-FEM in Matlab. Comput. Methods Appl. Math. 11(4): 460-490 (2011) - [j12]Christoph Ortner, Dirk Praetorius:
On the Convergence of Adaptive Nonconforming Finite Element Methods for a Class of Convex Variational Problems. SIAM J. Numer. Anal. 49(1): 346-367 (2011) - 2010
- [j11]Othmar Koch, Roswitha März, Dirk Praetorius, Ewa Weinmüller:
Collocation methods for index 1 DAEs with a singularity of the first kind. Math. Comput. 79(269): 281-304 (2010) - [j10]Samuel Ferraz-Leite, Christoph Ortner, Dirk Praetorius:
Convergence of simple adaptive Galerkin schemes based on h - h/2 error estimators. Numerische Mathematik 116(2): 291-316 (2010)
2000 – 2009
- 2008
- [j9]Samuel Ferraz-Leite, Dirk Praetorius:
Simple a posteriori error estimators for the h-version of the boundary element method. Computing 83(4): 135-162 (2008) - [j8]Christoph Erath, Dirk Praetorius:
A Posteriori Error Estimate and Adaptive Mesh Refinement for the Cell-Centered Finite Volume Method for Elliptic Boundary Value Problems. SIAM J. Numer. Anal. 47(1): 109-135 (2008) - 2007
- [j7]Carsten Carstensen, Dirk Praetorius:
Averaging Techniques for the A Posteriori BEM Error Control for a Hypersingular Integral Equation in Two Dimensions. SIAM J. Sci. Comput. 29(2): 782-810 (2007) - 2006
- [j6]Carsten Carstensen, Dirk Praetorius:
Averaging Techniques for the Effective Numerical Solution of Symm's Integral Equation of the First Kind. SIAM J. Sci. Comput. 27(4): 1226-1260 (2006) - 2005
- [j5]Nikola Popovic, Dirk Praetorius:
Applications of H -Matrix Techniques in Micromagnetics. Computing 74(3): 177-204 (2005) - [j4]Winfried Auzinger, Othmar Koch, Dirk Praetorius, Ewa Weinmüller:
New a posteriori error estimates for singular boundary value problems. Numer. Algorithms 40(1): 79-100 (2005) - [j3]Carsten Carstensen, Dirk Praetorius:
Numerical Analysis for a Macroscopic Model in Micromagnetics. SIAM J. Numer. Anal. 42(6): 2633-2651 (2005) - [c1]Nikola Popovic, Dirk Praetorius:
H-Matrix Techniques for Stray-Field Computations in Computational Micromagnetics. LSSC 2005: 102-110 - 2004
- [j2]Carsten Carstensen, Matthias Maischak, Dirk Praetorius, Ernst P. Stephan:
Residual-based a posteriori error estimate for hypersingular equation on surfaces. Numerische Mathematik 97(3): 397-425 (2004) - 2003
- [j1]Carsten Carstensen, Dirk Praetorius:
A Posteriori Error Control in Adaptive Qualocation Boundary Element Analysis for a Logarithmic-Kernel Integral Equation of the First Kind. SIAM J. Sci. Comput. 25(1): 259-283 (2003)
Coauthor Index
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