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Author ID: praetorius.dirk Recent zbMATH articles by "Praetorius, Dirk"
Published as: Praetorius, Dirk; Praetorius, D.
External Links: MGP · ORCID
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Serials

11 Numerische Mathematik
9 Computers & Mathematics with Applications
9 SIAM Journal on Numerical Analysis
8 Computational Methods in Applied Mathematics
7 Computer Methods in Applied Mechanics and Engineering
7 IMA Journal of Numerical Analysis
6 Mathematics of Computation
6 Applied Numerical Mathematics
5 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
4 Applicable Analysis
3 SIAM Journal on Scientific Computing
3 Engineering Analysis with Boundary Elements
3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
2 Journal of Computational Physics
2 Calcolo
2 Computing
2 Journal of Computational and Applied Mathematics
2 Constructive Approximation
2 Computational Mechanics
2 Numerical Methods for Partial Differential Equations
2 Numerical Algorithms
2 Continuum Mechanics and Thermodynamics
2 ETNA. Electronic Transactions on Numerical Analysis
1 Mathematical Methods in the Applied Sciences
1 Colloquium Mathematicum
1 Journal of Differential Equations
1 Zeitschrift für Analysis und ihre Anwendungen
1 Computer Aided Geometric Design
1 Journal of Integral Equations and Applications
1 Applied Mathematical Modelling
1 Advances in Computational Mathematics
1 Nonlinear Analysis. Real World Applications
1 Archives of Computational Methods in Engineering
1 Journal of Numerical Mathematics
1 International Journal of Numerical Analysis and Modeling
1 PAMM. Proceedings in Applied Mathematics and Mechanics
1 SIAM/ASA Journal on Uncertainty Quantification

Publications by Year

Citations contained in zbMATH Open

107 Publications have been cited 1,160 times in 417 Documents Cited by Year
Axioms of adaptivity. Zbl 1350.65119
Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D.
112
2014
Efficient implementation of adaptive P1-FEM in Matlab. Zbl 1284.65197
Funken, Stefan; Praetorius, Dirk; Wissgott, Philipp
46
2011
On 2D newest vertex bisection: optimality of mesh-closure and \(H ^{1}\)-stability of \(L _{2}\)-projection. Zbl 1302.65267
Karkulik, Michael; Pavlicek, David; Praetorius, Dirk
46
2013
Adaptive FEM with optimal convergence rates for a certain class of nonsymmetric and possibly nonlinear problems. Zbl 1300.65086
Feischl, M.; Führer, T.; Praetorius, D.
39
2014
Quasi-optimal convergence rate for an adaptive boundary element method. Zbl 1273.65186
Feischl, M.; Karkulik, M.; Melenk, J. M.; Praetorius, D.
37
2013
Residual-based a posteriori error estimate for hypersingular equation on surfaces. Zbl 1063.65116
Carstensen, Carsten; Maischak, M.; Praetorius, D.; Stephan, E. P.
31
2004
Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity. Zbl 1312.74031
Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk
26
2013
Efficiency and optimality of some weighted-residual error estimator for adaptive 2D boundary element methods. Zbl 1285.65070
Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk
25
2013
Simple a posteriori error estimators for the \(h\)-version of the boundary element method. Zbl 1175.65126
Ferraz-Leite, S.; Praetorius, D.
25
2008
Convergence of simple adaptive Galerkin schemes based on \(h - h/2\) error estimators. Zbl 1198.65213
Ferraz-Leite, S.; Ortner, C.; Praetorius, D.
24
2010
An abstract analysis of optimal goal-oriented adaptivity. Zbl 1382.65392
Feischl, Michael; Praetorius, Dirk; van der Zee, Kristoffer G.
24
2016
Averaging techniques for the effective numerical solution of Symm’s integral equation of the first kind. Zbl 1105.65124
Carstensen, Carsten; Praetorius, Dirk
24
2006
Energy norm based a posteriori error estimation for boundary element methods in two dimensions. Zbl 1177.65192
Erath, C.; Ferraz-Leite, S.; Funken, S.; Praetorius, D.
21
2009
Estimator reduction and convergence of adaptive BEM. Zbl 1237.65131
Aurada, Markus; Ferraz-Leite, Samuel; Praetorius, Dirk
20
2012
Adaptive IGAFEM with optimal convergence rates: hierarchical B-splines. Zbl 1376.41006
Gantner, Gregor; Haberlik, Daniel; Praetorius, Dirk
20
2017
Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. I: Weakly-singular integral equation. Zbl 1314.65161
Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk
18
2014
Energy norm based error estimators for adaptive BEM for hypersingular integral equations. Zbl 1320.65184
Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk
18
2015
Simple error estimators for the Galerkin BEM for some hypersingular integral equation in 2D. Zbl 1278.65168
Erath, C.; Funken, S.; Goldenits, P.; Praetorius, D.
17
2013
Local inverse estimates for non-local boundary integral operators. Zbl 1368.65242
Aurada, M.; Feischl, M.; Führer, T.; Karkulik, M.; Melenk, J. M.; Praetorius, D.
17
2017
Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations. Zbl 1362.65131
Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk
17
2017
Averaging techniques for the a posteriori BEM error control for a hypersingular integral equation in two dimensions. Zbl 1140.65089
Carstensen, Carsten; Praetorius, Dirk
17
2007
Adaptive 2D IGA boundary element methods. Zbl 1403.65267
Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk
16
2016
Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations. Zbl 1425.65200
Feischl, Michael; Gantner, Gregor; Praetorius, Dirk
16
2015
Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. II: Hyper-singular integral equation. Zbl 1312.65173
Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, J. Markus; Praetorius, Dirk
16
2015
HILBERT – a MATLAB implementation of adaptive 2D-BEM. \(\underline {\text H}\)ilbert \(\underline {\text I}\)s a \(\underline {\text L}\)ovely \(\underline {\text B}\)oundary \(\underline {\text E}\)lement \(\underline {\text R}\)esearch \(\underline {\text T}\)ool. Zbl 1298.65183
Aurada, Markus; Ebner, Michael; Feischl, Michael; Ferraz-Leite, Samuel; Führer, Thomas; Goldenits, Petra; Karkulik, Michael; Mayr, Markus; Praetorius, Dirk
15
2014
Each \(H^{1/2}\)-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in \(\mathbb R^d\). Zbl 1275.65078
Aurada, M.; Feischl, M.; Kemetmüller, J.; Page, M.; Praetorius, D.
14
2013
Adaptive boundary element methods. A posteriori error estimators, adaptivity, convergence, and implementation. Zbl 1348.65172
Feischl, Michael; Führer, Thomas; Heuer, Norbert; Karkulik, Michael; Praetorius, Dirk
14
2015
Rate optimal adaptive FEM with inexact solver for nonlinear operators. Zbl 1477.65212
Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Stiftner, Bernhard
14
2018
Spin-polarized transport in ferromagnetic multilayers: an unconditionally convergent FEM integrator. Zbl 1361.82041
Abert, Claas; Hrkac, Gino; Page, Marcus; Praetorius, Dirk; Ruggeri, Michele; Suess, Dieter
14
2014
Multiscale modeling in micromagnetics: existence of solutions and numerical integration. Zbl 1320.35336
Bruckner, F.; Suess, D.; Feischl, M.; Führer, T.; Goldenits, P.; Page, M.; Praetorius, D.; Ruggeri, M.
13
2014
Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data. Zbl 1291.65341
Feischl, M.; Page, M.; Praetorius, D.
13
2014
\(\mathcal {H}\)-matrix approximability of the inverses of FEM matrices. Zbl 1334.65192
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
13
2015
Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems. Zbl 1276.65066
Aurada, Markus; Feischl, Michael; Praetorius, Dirk
12
2012
Averaging techniques for a posteriori error control in finite element and boundary element analysis. Zbl 1298.65161
Carstensen, Carsten; Praetorius, Dirk
11
2007
Dörfler marking with minimal cardinality is a linear complexity problem. Zbl 1446.65190
Pfeiler, Carl-Martin; Praetorius, Dirk
11
2020
Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems. Zbl 1439.65148
Bespalov, Alex; Haberl, Alexander; Praetorius, Dirk
11
2017
Analysis of the operator \(\Delta^{-1}\text{div}\) arising in magnetic models. Zbl 1137.35342
Praetorius, Dirk
11
2004
Numerical analysis for a macroscopic model in micromagnetics. Zbl 1088.78009
Carstensen, Carsten; Praetorius, Dirk
10
2005
Adaptive BEM with inexact PCG solver yields almost optimal computational costs. Zbl 1412.65233
Führer, Thomas; Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan
10
2019
On the convergence of adaptive nonconforming finite element methods for a class of convex variational problems. Zbl 1232.49034
Ortner, Christoph; Praetorius, Dirk
9
2011
Existence of \(\mathcal{H}\)-matrix approximants to the inverses of BEM matrices: the simple-layer operator. Zbl 1327.65253
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
9
2016
A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equations. Zbl 1327.65233
Baňas, Lubomir; Page, Marcus; Praetorius, Dirk
9
2015
On a decoupled linear FEM integrator for eddy-current-LLG. Zbl 1316.65087
Le, Kim-Ngan; Page, Marcus; Praetorius, Dirk; Tran, Thanh
9
2015
Convergence of an implicit-explicit midpoint scheme for computational micromagnetics. Zbl 1409.65075
Praetorius, Dirk; Ruggeri, Michele; Stiftner, Bernhard
9
2018
Convergence of adaptive BEM and adaptive FEM-BEM coupling for estimators without \(h\)-weighting factor. Zbl 1303.65091
Feischl, Michael; Führer, Thomas; Mitscha-Eibl, Gregor; Praetorius, Dirk; Stephan, Ernst P.
8
2014
Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh-refinement. Zbl 1280.65116
Karkulik, Michael; Of, Günther; Praetorius, Dirk
8
2013
Convergence of adaptive stochastic Galerkin FEM. Zbl 1425.65146
Bespalov, Alex; Praetorius, Dirk; Rocchi, Leonardo; Ruggeri, Michele
8
2019
Adaptive boundary element methods for optimal convergence of point errors. Zbl 1338.65259
Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Führer, Thomas
8
2016
Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation. Zbl 1466.65127
Di Fratta, Giovanni; Pfeiler, Carl-Martin; Praetorius, Dirk; Ruggeri, Michele; Stiftner, Bernhard
7
2020
Existence of \(\mathcal{H}\)-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator. Zbl 1433.65324
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
7
2017
A decoupled and unconditionally convergent linear FEM integrator for the Landau-Lifshitz-Gilbert equation with magnetostriction. Zbl 1334.78040
Baňas, Ľubomír; Page, Marcus; Praetorius, Dirk; Rochat, Jonathan
7
2014
Collocation methods for index 1 DAEs with a singularity of the first kind. Zbl 1196.65134
Koch, Othmar; März, Roswitha; Praetorius, Dirk; Weinmüller, Ewa
7
2010
Convergence of adaptive boundary element methods. Zbl 1238.65124
Carstensen, Carsten; Praetorius, Dirk
7
2012
Adaptive vertex-centered finite volume methods with convergence rates. Zbl 1416.65410
Erath, Christoph; Praetorius, Dirk
7
2016
Applications of \(\mathcal H\)-matrix techniques in micromagnetics. Zbl 1070.78011
Popović, N.; Praetorius, D.
7
2005
Adaptive isogeometric boundary element methods with local smoothness control. Zbl 07205673
Gantner, Gregor; Praetorius, Dirk; Schimanko, Stefan
7
2020
Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations. Zbl 1372.65317
Feischl, Michael; Führer, Thomas; Praetorius, Dirk; Stephan, Ernst P.
6
2017
A posteriori error estimates for the Johnson-Nédélec FEM-BEM coupling. Zbl 1245.65154
Aurada, M.; Feischl, M.; Karkulik, M.; Praetorius, Dirk
6
2012
Convergence of adaptive BEM for some mixed boundary value problem. Zbl 1242.65220
Aurada, M.; Ferraz-Leite, S.; Goldenits, P.; Karkulik, M.; Mayr, M.; Praetorius, D.
6
2012
ZZ-type a posteriori error estimators for adaptive boundary element methods on a curve. Zbl 1287.65102
Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk
6
2014
Effective simulation of a macroscopic model for stationary micromagnetics. Zbl 1063.78016
Carstensen, Carsten; Praetorius, Dirk
6
2005
Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs. Zbl 1440.65184
Bespalov, Alex; Praetorius, Dirk; Rocchi, Leonardo; Ruggeri, Michele
6
2019
Simultaneous quasi-optimal convergence rates in FEM-BEM coupling. Zbl 1359.65263
Melenk, J. M.; Praetorius, D.; Wohlmuth, B.
6
2017
Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics. Zbl 1415.78008
Hrkac, Gino; Pfeiler, Carl-Martin; Praetorius, Dirk; Ruggeri, Michele; Segatti, Antonio; Stiftner, Bernhard
6
2019
New a posteriori error estimates for singular boundary value problems. Zbl 1082.65079
Auzinger, Winfried; Koch, Othmar; Praetorius, Dirk; Weinmüller, Ewa
5
2005
A posteriori error estimate and adaptive mesh refinement for the cell-centered finite volume method for elliptic boundary value problems. Zbl 1188.65148
Erath, Christoph; Praetorius, Dirk
5
2009
Convergence of adaptive FEM for some elliptic obstacle problem. Zbl 1262.65156
Page, M.; Praetorius, D.
5
2013
Adaptive IGAFEM with optimal convergence rates: T-splines. Zbl 07242739
Gantner, Gregor; Praetorius, Dirk
5
2020
Energy contraction and optimal convergence of adaptive iterative linearized finite element methods. Zbl 1480.35214
Heid, Pascal; Praetorius, Dirk; Wihler, Thomas P.
5
2021
Stability of symmetric and nonsymmetric FEM-BEM couplings for nonlinear elasticity problems. Zbl 1439.74410
Feischl, M.; Führer, T.; Karkulik, M.; Praetorius, D.
5
2015
Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements. Zbl 1365.65253
Feischl, Michael; Führer, Thomas; Praetorius, Dirk; Stephan, Ernst P.
5
2017
Adaptive BEM with optimal convergence rates for the Helmholtz equation. Zbl 1440.65259
Bespalov, Alex; Betcke, Timo; Haberl, Alexander; Praetorius, Dirk
5
2019
Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods. Zbl 1441.65114
Führer, Thomas; Gantner, Gregor; Praetorius, Dirk; Schimanko, Stefan
5
2019
Optimal convergence behavior of adaptive FEM driven by simple \((h-h/2)\)-type error estimators. Zbl 1443.65294
Erath, Christoph; Gantner, Gregor; Praetorius, Dirk
4
2020
Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics. Zbl 1451.35205
Di Fratta, Giovanni; Innerberger, Michael; Praetorius, Dirk
4
2020
A posteriori error control in adaptive qualocation boundary element analysis for a logarithmic-kernel integral equation of the first kind. Zbl 1042.65084
Carstensen, Carsten; Praetorius, Dirk
4
2003
Optimal convergence rates for goal-oriented FEM with quadratic goal functional. Zbl 1476.65290
Becker, Roland; Innerberger, Michael; Praetorius, Dirk
4
2021
Convergence of adaptive FEM for some elliptic obstacle problem with inhomogeneous Dirichlet data. Zbl 1310.65144
Feischl, Michael; Page, Marcus; Praetorius, Dirk
4
2014
A linear Uzawa-type FEM-BEM solver for nonlinear transmission problems. Zbl 1415.65247
Führer, Thomas; Praetorius, Dirk
4
2018
Adaptive boundary element methods for the computation of the electrostatic capacity on complex polyhedra. Zbl 1453.78012
Betcke, Timo; Haberl, Alexander; Praetorius, Dirk
3
2019
Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian. Zbl 1478.65121
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
3
2021
Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics. Zbl 1263.78017
Ferraz-Leite, Samuel; Melenk, Jens Markus; Praetorius, Dirk
3
2012
FEM-BEM coupling for the large-body limit in micromagnetics. Zbl 1310.78014
Aurada, M.; Melenk, J. M.; Praetorius, D.
3
2015
Rate optimality of adaptive finite element methods with respect to overall computational costs. Zbl 1468.65189
Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan
3
2021
Optimal adaptivity for the SUPG finite element method. Zbl 1441.65101
Erath, Christoph; Praetorius, Dirk
3
2019
Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. I: Analysis. Zbl 1160.74355
Popović, Nikola; Praetorius, Dirk; Schlömerkemper, Anja
3
2007
Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. II: Numerical simulation. Zbl 1160.74356
Popović, Nikola; Praetorius, Dirk; Schlömerkemper, Anja
3
2007
Adaptive vertex-centered finite volume methods for general second-order linear elliptic partial differential equations. Zbl 1466.65167
Erath, Christoph; Praetorius, Dirk
2
2019
Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver. Zbl 1468.65191
Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan; Vohralík, Martin
2
2021
Stabilisation yields strong convergence of macroscopic magnetisation vectors for micromagnetics without exchange energy. Zbl 1247.78051
Carstensen, C.; Praetorius, D.
2
2012
A short note on plain convergence of adaptive least-squares finite element methods. Zbl 1451.65189
Führer, Thomas; Praetorius, Dirk
2
2020
Mixed conforming elements for the large-body limit in micromagnetics. Zbl 1285.65076
Aurada, Markus; Melenk, Jens M.; Praetorius, Dirk
2
2014
A new proof for existence of \(\mathcal H\)-matrix approximants to the inverse of FEM matrices: the Dirichlet problem for the Laplacian. Zbl 1282.65153
Faustmann, Markus; Melenk, Jens M.; Praetorius, Dirk
2
2014
Adaptive Uzawa algorithm for the Stokes equation. Zbl 1434.65248
Di Fratta, Giovanni; Führer, Thomas; Gantner, Gregor; Praetorius, Dirk
2
2019
Instance-optimal goal-oriented adaptivity. Zbl 1474.65440
Innerberger, Michael; Praetorius, Dirk
2
2021
Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics. Zbl 1453.82102
Kraus, Johannes; Pfeiler, Carl-Martin; Praetorius, Dirk; Ruggeri, Michele; Stiftner, Bernhard
1
2019
Céa-type quasi-optimality and convergence rates for (adaptive) vertex-centered FVM. Zbl 1372.65294
Erath, Christoph; Praetorius, Dirk
1
2017
Remarks and examples concerning distance ellipsoids. Zbl 1017.46006
Praetorius, Dirk
1
2002
Magnetic force formulae for magnets at small distances. Zbl 1391.78003
Popović, Nikola; Praetorius, Dirk; Schlömerkemper, Anja
1
2005
The saturation assumption yields optimal convergence of two-level adaptive BEM. Zbl 1440.65263
Praetorius, Dirk; Ruggeri, Michele; Stephan, Ernst P.
1
2020
Adaptive BEM for elliptic PDE systems. I: Abstract framework, for weakly-singular integral equations. Zbl 1490.65248
Gantner, Gregor; Praetorius, Dirk
1
2022
Plain convergence of adaptive algorithms without exploiting reliability and efficiency. Zbl 07524720
Gantner, Gregor; Praetorius, Dirk
1
2022
Adaptive BEM for elliptic PDE systems. II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations. Zbl 1490.65299
Gantner, Gregor; Praetorius, Dirk
1
2022
Micromagnetics of thin films in the presence of Dzyaloshinskii-Moriya interaction. Zbl 1492.78005
Davoli, Elisa; Di Fratta, Giovanni; Praetorius, Dirk; Ruggeri, Michele
1
2022
Energy contraction and optimal convergence of adaptive iterative linearized finite element methods. Zbl 1480.35214
Heid, Pascal; Praetorius, Dirk; Wihler, Thomas P.
5
2021
Optimal convergence rates for goal-oriented FEM with quadratic goal functional. Zbl 1476.65290
Becker, Roland; Innerberger, Michael; Praetorius, Dirk
4
2021
Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian. Zbl 1478.65121
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
3
2021
Rate optimality of adaptive finite element methods with respect to overall computational costs. Zbl 1468.65189
Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan
3
2021
Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver. Zbl 1468.65191
Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan; Vohralík, Martin
2
2021
Instance-optimal goal-oriented adaptivity. Zbl 1474.65440
Innerberger, Michael; Praetorius, Dirk
2
2021
Dörfler marking with minimal cardinality is a linear complexity problem. Zbl 1446.65190
Pfeiler, Carl-Martin; Praetorius, Dirk
11
2020
Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation. Zbl 1466.65127
Di Fratta, Giovanni; Pfeiler, Carl-Martin; Praetorius, Dirk; Ruggeri, Michele; Stiftner, Bernhard
7
2020
Adaptive isogeometric boundary element methods with local smoothness control. Zbl 07205673
Gantner, Gregor; Praetorius, Dirk; Schimanko, Stefan
7
2020
Adaptive IGAFEM with optimal convergence rates: T-splines. Zbl 07242739
Gantner, Gregor; Praetorius, Dirk
5
2020
Optimal convergence behavior of adaptive FEM driven by simple \((h-h/2)\)-type error estimators. Zbl 1443.65294
Erath, Christoph; Gantner, Gregor; Praetorius, Dirk
4
2020
Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics. Zbl 1451.35205
Di Fratta, Giovanni; Innerberger, Michael; Praetorius, Dirk
4
2020
A short note on plain convergence of adaptive least-squares finite element methods. Zbl 1451.65189
Führer, Thomas; Praetorius, Dirk
2
2020
The saturation assumption yields optimal convergence of two-level adaptive BEM. Zbl 1440.65263
Praetorius, Dirk; Ruggeri, Michele; Stephan, Ernst P.
1
2020
Adaptive BEM with inexact PCG solver yields almost optimal computational costs. Zbl 1412.65233
Führer, Thomas; Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan
10
2019
Convergence of adaptive stochastic Galerkin FEM. Zbl 1425.65146
Bespalov, Alex; Praetorius, Dirk; Rocchi, Leonardo; Ruggeri, Michele
8
2019
Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs. Zbl 1440.65184
Bespalov, Alex; Praetorius, Dirk; Rocchi, Leonardo; Ruggeri, Michele
6
2019
Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics. Zbl 1415.78008
Hrkac, Gino; Pfeiler, Carl-Martin; Praetorius, Dirk; Ruggeri, Michele; Segatti, Antonio; Stiftner, Bernhard
6
2019
Adaptive BEM with optimal convergence rates for the Helmholtz equation. Zbl 1440.65259
Bespalov, Alex; Betcke, Timo; Haberl, Alexander; Praetorius, Dirk
5
2019
Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods. Zbl 1441.65114
Führer, Thomas; Gantner, Gregor; Praetorius, Dirk; Schimanko, Stefan
5
2019
Adaptive boundary element methods for the computation of the electrostatic capacity on complex polyhedra. Zbl 1453.78012
Betcke, Timo; Haberl, Alexander; Praetorius, Dirk
3
2019
Optimal adaptivity for the SUPG finite element method. Zbl 1441.65101
Erath, Christoph; Praetorius, Dirk
3
2019
Adaptive vertex-centered finite volume methods for general second-order linear elliptic partial differential equations. Zbl 1466.65167
Erath, Christoph; Praetorius, Dirk
2
2019
Adaptive Uzawa algorithm for the Stokes equation. Zbl 1434.65248
Di Fratta, Giovanni; Führer, Thomas; Gantner, Gregor; Praetorius, Dirk
2
2019
Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics. Zbl 1453.82102
Kraus, Johannes; Pfeiler, Carl-Martin; Praetorius, Dirk; Ruggeri, Michele; Stiftner, Bernhard
1
2019
Rate optimal adaptive FEM with inexact solver for nonlinear operators. Zbl 1477.65212
Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Stiftner, Bernhard
14
2018
Convergence of an implicit-explicit midpoint scheme for computational micromagnetics. Zbl 1409.65075
Praetorius, Dirk; Ruggeri, Michele; Stiftner, Bernhard
9
2018
A linear Uzawa-type FEM-BEM solver for nonlinear transmission problems. Zbl 1415.65247
Führer, Thomas; Praetorius, Dirk
4
2018
Adaptive IGAFEM with optimal convergence rates: hierarchical B-splines. Zbl 1376.41006
Gantner, Gregor; Haberlik, Daniel; Praetorius, Dirk
20
2017
Local inverse estimates for non-local boundary integral operators. Zbl 1368.65242
Aurada, M.; Feischl, M.; Führer, T.; Karkulik, M.; Melenk, J. M.; Praetorius, D.
17
2017
Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations. Zbl 1362.65131
Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk
17
2017
Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems. Zbl 1439.65148
Bespalov, Alex; Haberl, Alexander; Praetorius, Dirk
11
2017
Existence of \(\mathcal{H}\)-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator. Zbl 1433.65324
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
7
2017
Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations. Zbl 1372.65317
Feischl, Michael; Führer, Thomas; Praetorius, Dirk; Stephan, Ernst P.
6
2017
Simultaneous quasi-optimal convergence rates in FEM-BEM coupling. Zbl 1359.65263
Melenk, J. M.; Praetorius, D.; Wohlmuth, B.
6
2017
Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements. Zbl 1365.65253
Feischl, Michael; Führer, Thomas; Praetorius, Dirk; Stephan, Ernst P.
5
2017
Céa-type quasi-optimality and convergence rates for (adaptive) vertex-centered FVM. Zbl 1372.65294
Erath, Christoph; Praetorius, Dirk
1
2017
An abstract analysis of optimal goal-oriented adaptivity. Zbl 1382.65392
Feischl, Michael; Praetorius, Dirk; van der Zee, Kristoffer G.
24
2016
Adaptive 2D IGA boundary element methods. Zbl 1403.65267
Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk
16
2016
Existence of \(\mathcal{H}\)-matrix approximants to the inverses of BEM matrices: the simple-layer operator. Zbl 1327.65253
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
9
2016
Adaptive boundary element methods for optimal convergence of point errors. Zbl 1338.65259
Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Führer, Thomas
8
2016
Adaptive vertex-centered finite volume methods with convergence rates. Zbl 1416.65410
Erath, Christoph; Praetorius, Dirk
7
2016
Energy norm based error estimators for adaptive BEM for hypersingular integral equations. Zbl 1320.65184
Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk
18
2015
Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations. Zbl 1425.65200
Feischl, Michael; Gantner, Gregor; Praetorius, Dirk
16
2015
Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. II: Hyper-singular integral equation. Zbl 1312.65173
Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, J. Markus; Praetorius, Dirk
16
2015
Adaptive boundary element methods. A posteriori error estimators, adaptivity, convergence, and implementation. Zbl 1348.65172
Feischl, Michael; Führer, Thomas; Heuer, Norbert; Karkulik, Michael; Praetorius, Dirk
14
2015
\(\mathcal {H}\)-matrix approximability of the inverses of FEM matrices. Zbl 1334.65192
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
13
2015
A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equations. Zbl 1327.65233
Baňas, Lubomir; Page, Marcus; Praetorius, Dirk
9
2015
On a decoupled linear FEM integrator for eddy-current-LLG. Zbl 1316.65087
Le, Kim-Ngan; Page, Marcus; Praetorius, Dirk; Tran, Thanh
9
2015
Stability of symmetric and nonsymmetric FEM-BEM couplings for nonlinear elasticity problems. Zbl 1439.74410
Feischl, M.; Führer, T.; Karkulik, M.; Praetorius, D.
5
2015
FEM-BEM coupling for the large-body limit in micromagnetics. Zbl 1310.78014
Aurada, M.; Melenk, J. M.; Praetorius, D.
3
2015
Erratum to: “On 2D newest vertex bisection: optimality of mesh-closure and \(H^1\)-stability of \(L_2\)-projection”. Zbl 1331.65167
Karkulik, Michael; Pavlicek, David; Praetorius, Dirk
1
2015
Axioms of adaptivity. Zbl 1350.65119
Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D.
112
2014
Adaptive FEM with optimal convergence rates for a certain class of nonsymmetric and possibly nonlinear problems. Zbl 1300.65086
Feischl, M.; Führer, T.; Praetorius, D.
39
2014
Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. I: Weakly-singular integral equation. Zbl 1314.65161
Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk
18
2014
HILBERT – a MATLAB implementation of adaptive 2D-BEM. \(\underline {\text H}\)ilbert \(\underline {\text I}\)s a \(\underline {\text L}\)ovely \(\underline {\text B}\)oundary \(\underline {\text E}\)lement \(\underline {\text R}\)esearch \(\underline {\text T}\)ool. Zbl 1298.65183
Aurada, Markus; Ebner, Michael; Feischl, Michael; Ferraz-Leite, Samuel; Führer, Thomas; Goldenits, Petra; Karkulik, Michael; Mayr, Markus; Praetorius, Dirk
15
2014
Spin-polarized transport in ferromagnetic multilayers: an unconditionally convergent FEM integrator. Zbl 1361.82041
Abert, Claas; Hrkac, Gino; Page, Marcus; Praetorius, Dirk; Ruggeri, Michele; Suess, Dieter
14
2014
Multiscale modeling in micromagnetics: existence of solutions and numerical integration. Zbl 1320.35336
Bruckner, F.; Suess, D.; Feischl, M.; Führer, T.; Goldenits, P.; Page, M.; Praetorius, D.; Ruggeri, M.
13
2014
Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data. Zbl 1291.65341
Feischl, M.; Page, M.; Praetorius, D.
13
2014
Convergence of adaptive BEM and adaptive FEM-BEM coupling for estimators without \(h\)-weighting factor. Zbl 1303.65091
Feischl, Michael; Führer, Thomas; Mitscha-Eibl, Gregor; Praetorius, Dirk; Stephan, Ernst P.
8
2014
A decoupled and unconditionally convergent linear FEM integrator for the Landau-Lifshitz-Gilbert equation with magnetostriction. Zbl 1334.78040
Baňas, Ľubomír; Page, Marcus; Praetorius, Dirk; Rochat, Jonathan
7
2014
ZZ-type a posteriori error estimators for adaptive boundary element methods on a curve. Zbl 1287.65102
Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk
6
2014
Convergence of adaptive FEM for some elliptic obstacle problem with inhomogeneous Dirichlet data. Zbl 1310.65144
Feischl, Michael; Page, Marcus; Praetorius, Dirk
4
2014
Mixed conforming elements for the large-body limit in micromagnetics. Zbl 1285.65076
Aurada, Markus; Melenk, Jens M.; Praetorius, Dirk
2
2014
A new proof for existence of \(\mathcal H\)-matrix approximants to the inverse of FEM matrices: the Dirichlet problem for the Laplacian. Zbl 1282.65153
Faustmann, Markus; Melenk, Jens M.; Praetorius, Dirk
2
2014
On 2D newest vertex bisection: optimality of mesh-closure and \(H ^{1}\)-stability of \(L _{2}\)-projection. Zbl 1302.65267
Karkulik, Michael; Pavlicek, David; Praetorius, Dirk
46
2013
Quasi-optimal convergence rate for an adaptive boundary element method. Zbl 1273.65186
Feischl, M.; Karkulik, M.; Melenk, J. M.; Praetorius, D.
37
2013
Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity. Zbl 1312.74031
Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk
26
2013
Efficiency and optimality of some weighted-residual error estimator for adaptive 2D boundary element methods. Zbl 1285.65070
Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk
25
2013
Simple error estimators for the Galerkin BEM for some hypersingular integral equation in 2D. Zbl 1278.65168
Erath, C.; Funken, S.; Goldenits, P.; Praetorius, D.
17
2013
Each \(H^{1/2}\)-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in \(\mathbb R^d\). Zbl 1275.65078
Aurada, M.; Feischl, M.; Kemetmüller, J.; Page, M.; Praetorius, D.
14
2013
Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh-refinement. Zbl 1280.65116
Karkulik, Michael; Of, Günther; Praetorius, Dirk
8
2013
Convergence of adaptive FEM for some elliptic obstacle problem. Zbl 1262.65156
Page, M.; Praetorius, D.
5
2013
Estimator reduction and convergence of adaptive BEM. Zbl 1237.65131
Aurada, Markus; Ferraz-Leite, Samuel; Praetorius, Dirk
20
2012
Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems. Zbl 1276.65066
Aurada, Markus; Feischl, Michael; Praetorius, Dirk
12
2012
Convergence of adaptive boundary element methods. Zbl 1238.65124
Carstensen, Carsten; Praetorius, Dirk
7
2012
A posteriori error estimates for the Johnson-Nédélec FEM-BEM coupling. Zbl 1245.65154
Aurada, M.; Feischl, M.; Karkulik, M.; Praetorius, Dirk
6
2012
Convergence of adaptive BEM for some mixed boundary value problem. Zbl 1242.65220
Aurada, M.; Ferraz-Leite, S.; Goldenits, P.; Karkulik, M.; Mayr, M.; Praetorius, D.
6
2012
Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics. Zbl 1263.78017
Ferraz-Leite, Samuel; Melenk, Jens Markus; Praetorius, Dirk
3
2012
Stabilisation yields strong convergence of macroscopic magnetisation vectors for micromagnetics without exchange energy. Zbl 1247.78051
Carstensen, C.; Praetorius, D.
2
2012
Efficient implementation of adaptive P1-FEM in Matlab. Zbl 1284.65197
Funken, Stefan; Praetorius, Dirk; Wissgott, Philipp
46
2011
On the convergence of adaptive nonconforming finite element methods for a class of convex variational problems. Zbl 1232.49034
Ortner, Christoph; Praetorius, Dirk
9
2011
Convergence of simple adaptive Galerkin schemes based on \(h - h/2\) error estimators. Zbl 1198.65213
Ferraz-Leite, S.; Ortner, C.; Praetorius, D.
24
2010
Collocation methods for index 1 DAEs with a singularity of the first kind. Zbl 1196.65134
Koch, Othmar; März, Roswitha; Praetorius, Dirk; Weinmüller, Ewa
7
2010
Energy norm based a posteriori error estimation for boundary element methods in two dimensions. Zbl 1177.65192
Erath, C.; Ferraz-Leite, S.; Funken, S.; Praetorius, D.
21
2009
A posteriori error estimate and adaptive mesh refinement for the cell-centered finite volume method for elliptic boundary value problems. Zbl 1188.65148
Erath, Christoph; Praetorius, Dirk
5
2009
Simple a posteriori error estimators for the \(h\)-version of the boundary element method. Zbl 1175.65126
Ferraz-Leite, S.; Praetorius, D.
25
2008
Averaging techniques for the a posteriori BEM error control for a hypersingular integral equation in two dimensions. Zbl 1140.65089
Carstensen, Carsten; Praetorius, Dirk
17
2007
Averaging techniques for a posteriori error control in finite element and boundary element analysis. Zbl 1298.65161
Carstensen, Carsten; Praetorius, Dirk
11
2007
Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. I: Analysis. Zbl 1160.74355
Popović, Nikola; Praetorius, Dirk; Schlömerkemper, Anja
3
2007
Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. II: Numerical simulation. Zbl 1160.74356
Popović, Nikola; Praetorius, Dirk; Schlömerkemper, Anja
3
2007
Averaging techniques for the effective numerical solution of Symm’s integral equation of the first kind. Zbl 1105.65124
Carstensen, Carsten; Praetorius, Dirk
24
2006
\(\mathcal H\)-matrix techniques for stray-field computations in computational micromagnetics. Zbl 1142.78311
Popović, Nikola; Praetorius, Dirk
1
2006
Numerical analysis for a macroscopic model in micromagnetics. Zbl 1088.78009
Carstensen, Carsten; Praetorius, Dirk
10
2005
Applications of \(\mathcal H\)-matrix techniques in micromagnetics. Zbl 1070.78011
Popović, N.; Praetorius, D.
7
2005
Effective simulation of a macroscopic model for stationary micromagnetics. Zbl 1063.78016
Carstensen, Carsten; Praetorius, Dirk
6
2005
...and 7 more Documents
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Cited by 568 Authors

80 Praetorius, Dirk
28 Carstensen, Carsten
27 Feischl, Michael
27 Melenk, Jens Markus
24 Führer, Thomas
21 Karkulik, Michael
16 Gantner, Gregor
13 Erath, Christoph
12 Ruggeri, Michele
11 Faustmann, Markus
10 Heuer, Norbert
10 Stephan, Ernst Peter
9 Aurada, Markus
9 Haberl, Alexander
8 Nochetto, Ricardo Horacio
7 Bespalov, Alexei
7 Di Fratta, Giovanni
7 Ferraz-Leite, Samuel
7 Heid, Pascal
6 Chen, Jingrun
6 Funken, Stefan A.
6 Gimperlein, Heiko
6 Innerberger, Michael
6 Weinmüller, Ewa B.
5 Bringmann, Philipp
5 Giannelli, Carlotta
5 Langer, Ulrich
5 Rieder, Alexander
5 Schimanko, Stefan
5 Stevenson, Rob P.
5 Wihler, Thomas Pascal
4 Becker, Roland
4 Bertrand, Fleurianne
4 Boffi, Daniele
4 Bracco, Cesare
4 Gallistl, Dietmar
4 Gedicke, Joscha
4 Goldenits, Petra
4 Harbrecht, Helmut
4 Jerez-Hanckes, Carlos
4 Ma, Rui
4 Morgenstern, Philipp
4 Page, Marcus
4 Pfeiler, Carl-Martin
4 Schlömerkemper, Anja
4 Vazquez, Rafael
4 Vohralík, Martin
4 Wick, Thomas
4 Xu, Yifeng
3 Atroshchenko, Elena
3 Auzinger, Winfried
3 Banz, Lothar
3 Betcke, Timo
3 Bordas, Stéphane Pierre Alain
3 Buffa, Annalisa
3 Chung, Tsz Shun Eric
3 Dölz, Jürgen
3 Ern, Alexandre
3 Gaddam, Sharat
3 Gudi, Thirupathi
3 Hiptmair, Ralf
3 Koch, Othmar
3 Kreuzer, Christian
3 Kurz, Stefan
3 Leonel, Edson Denner
3 Li, Yuwen
3 März, Roswitha
3 Natarajan, Sundararajan
3 Of, Günther
3 Ortner, Christoph
3 Özdemir, Ceyhun
3 Parvizi, Maryam
3 Peterseim, Daniel
3 Pollock, Sara
3 Popović, Nikola
3 Repin, Sergeĭ Igorevich
3 Rodrigues Neto, Antônio
3 Sayas, Francisco-Javier
3 Schafelner, Andreas
3 Schmidt, Anja
3 Schorr, Robert
3 Schwab, Christoph
3 Stiftner, Bernhard
3 Verani, Marco
3 Wang, Cheng
3 Wu, Jiming
3 Xie, Changjian
3 Zhou, Yanhui
2 An, Rong
2 Angleitner, Niklas
2 Bagherzadeh, Amir Saboor
2 Bakry, Marc
2 Banjai, Lehel
2 Bebendorf, Mario
2 Bonito, Andrea
2 Borthagaray, Juan Pablo
2 Canuto, Claudio
2 Chaillat, Stéphanie
2 Chambolle, Antonin
2 Chaumont-Frelet, Théophile
...and 468 more Authors
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Cited in 83 Serials

48 Computers & Mathematics with Applications
36 Numerische Mathematik
31 SIAM Journal on Numerical Analysis
30 Computer Methods in Applied Mechanics and Engineering
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16 Journal of Computational Physics
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12 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
10 Journal of Scientific Computing
10 Engineering Analysis with Boundary Elements
9 Journal of Computational and Applied Mathematics
8 SIAM Journal on Scientific Computing
8 Advances in Computational Mathematics
7 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
6 Applied Mathematics and Computation
6 BIT
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4 Computational Mechanics
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4 Computing and Visualization in Science
3 Applied Mathematics Letters
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3 Foundations of Computational Mathematics
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