Andreas Veeser - Research
- finite element methods
- approximation properties of finite element spaces
- stability and quasi-optimality of generalized (Petrov-)Galerkin methods
- aposteriori error estimates and adaptivity
- variational inequalities
- mean curvature flow and crystal growth
Publications
In each section the publications appear in inverse chronological
order. If a publication or manuscript has no link or you do not have
access to the given one, please feel free to ask me for a hard- or
softcopy (contact).
- A posteriori error analysis for optimization with PDE constraints. Mathematical Control and Related Fields 15 (4), 1346-1375, 2025, with Fernando Gaspoz, Christian Kreuzer, and Winnifried Wollner.
- Adaptive finite element methods. Acta Numerica 33, 163-485 2024, with Andrea Bonito, Claudio Canuto, and Ricardo H. Nochetto.
- A nodally bound-preserving finite element method.
IMA Journal of Numerical Analysis 44 (4), 2198-2219, 2024, with Gabriel Barrenechea, Emmanuil Georgoulis, Tristan Pryer.
- Near-best adaptive approximation on conforming
meshes. Constructive Approximation 57, 327-349, 2023, with Peter Binev and Francesca Fierro.
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Oscillation in a posteriori error estimation.
Numer. Math. 148, 43-78, 2021, with Christian Kreuzer.
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Quasi-best approximation in optimization with PDE constraints.
Inverse Problems, 36, 014004, 2020,
with Fernando Gaspoz, Christian Kreuzer, and Winnifried Wollner.
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Quasi-optimal nonconforming methods for symmetric elliptic problems. II - Overconsistency and classical
nonconforming elements.
SIAM J. Numer. Anal., 57 (1), 266-292, 2019,
with Pietro Zanotti.
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Positivity preserving gradient approximation with linear finite elements. Comput. Methods Appl.
Math., 19 (2), 295-310, 2018/2019.
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Quasi-optimal nonconforming methods for symmetric elliptic problems. III - DG and other interior penalty methods.
SIAM J. Numer. Anal., 56 (5), 2871-2894, 2018,
with Pietro Zanotti.
- Quasi-optimal nonconforming methods for symmetric elliptic problems. I - Abstract theory. SIAM J. Numer. Anal., 56 (3), 1621-1642, 2018, with Pietro Zanotti.
- A posteriori error estimates with point sources in fractional Sobolev spaces. Numer. Methods Partial Differential Eq. 33 (4), 1018-1042, 2017, with Fernando Gaspoz and Pedro Morin.
- The L²-projection and quasi-optimality of Galerkin methods for parabolic equations. SIAM J. Numer. Anal. 54 (1), 317-340, 2016, with Francesca Tantardini.
- Robust localization of the best error with finite elements in the reaction-diffusion norm. Constructive Approximation 42 (2), 313-347, 2015, with Francesca Tantardini and Rüdiger Verfürth.
- Approximating gradients with continuous piecewise polynomial functions. Found. Comput. Math. 16, 723-750, 2016.
- An
efficient and reliable residual-type a posteriori error estimator for the Signorini problem. Numer. Math. 130 (2015), 151-197, with Rolf Krause and Mirjam Walloth.
- Poincaré constants for finite element stars.
IMA J. Numer. Anal. (2012) 32 (1): 30-47, with Rüdiger Verfürth.
- Hierarchical error
estimates for the energy functional in obstacle problems.
Numer. Math. 117 (2011), 653-677, with Qingsong Zou, Ralf Kornhuber,
and Carsten Gräser.
- Explicit
upper bounds for dual norms of residuals. SIAM
J. Numer. Anal. 47 (2009), 2387-2405, with Rüdiger
Verfürth.
- A
safeguarded dual weighted residual method. IMA
J. Numer. Anal. 29 (2009) 126-140, with Ricardo H. Nochetto and
Marco Verani.
- A
basic convergence result for conforming adaptive finite
elements. Math. Models Methods Appl. Sci. 18 (2008),
707-737, with Pedro Morin and Kunibert G. Siebert.
- A
unilaterally constrained quadratic minimization with adaptive finite
elements. SIAM J. Optim., 18 (2007), 260-289 , with
Kunibert G. Siebert.
- Pointwise a
posteriori error estimates for monotone semi-linear
equations. Numer. Math. 104 (2006), 515-538, with Ricardo
H. Nochetto, Alfred Schmidt and Kunibert G. Siebert.
- A
posteriori error estimators, gradient recovery by averaging, and
superconvergence. Numer. Math., 103 (2006), 267-298, with
Francesca Fierro.
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Locally efficient and reliable a posteriori error estimators for
Dirichlet problems. Math. Mod. Meth. Appl. Sci. 16
(2006), 319-346, with Roberta Sacchi.
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Fully localized a posteriori error estimators and barrier sets for
contact problems. SIAM J. Numer. Anal. 42 (2005),
2118-2135, with Ricardo H. Nochetto and Kunibert G. Siebert.
- A
posteriori error estimators for regularized total variation of
characteristic functions. SIAM J. Numer. Anal. 41 (2003),
2032-2055, with Francesca Fierro.
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Pointwise a posteriori error control for elliptic obstacle
problems. Numer. Math. 95 (2003), 163-195, with Ricardo
H. Nochetto and Kunibert G. Siebert.
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On the a posteriori error analysis for equations of prescribed mean
curvature. Math. Comp. 72 (2003), no. 244, 1611-1635,
with Francesca Fierro.
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Stability of flat interfaces during semidiscrete
solidification. M2AN Math. Model. Numer. Anal. 36 (2002),
573-595.
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Convergent adaptive finite elements for the nonlinear
Laplacian. Numer. Math. 92 (2002), 743-770.
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Efficient and reliable a posteriori error estimators for elliptic
obstacle problems. SIAM J. Numer. Anal. 39 (2001), no. 1,
146-167.
- Error estimates
for semi-discrete dendritic growth. Interfaces Free
Bound. 1 (1999), no. 2, 227-255.
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Adaptive tree approximation with finite element functions: a first look.
In: Daniele Di Pietro et al. (Eds.), Numerical methods for PDEs: State of the Art Techniques,
SEMA SIMAI Springer Series, vol 15. Springer, Cham, 249-284, 2018.
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Primer of adaptive finite element methods.
In: Multiscale and adaptivity: modeling, numerics and applications, G. Naldi, G. Russo (Eds.),
Springer Verlag Heidelberg, 125-225, 2012, with Ricardo H. Nochetto.
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Theory of adaptive finite element methods: an introduction.
In: Multiscale, nonlinear and adaptive approximation,
Ronald DeVore, Angela Kunoth (Eds.), Springer Verlag Heidelberg,
409-542, 2009, with Ricardo H. Nochetto and Kunibert G. Siebert.
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Simulation and Numerical Analysis of Dendritic Growth.
Ergodic theory, analysis, and efficient simulation of dynamical
systems, 225-252, Springer, Berlin, 2001, with Michael
Fried.
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Convergence of adaptive finite element methods with error-dominated oscillation.
In: Radu F., Kumar K., Berre I., Nordbotten J., Pop I. (eds),
Numerical Mathematics and Advanced Applications ENUMATH 2017.
Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham,
with Christian Kreuzer.
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Quasi-optimal nonconforming methods for second-order problems on domains with non-Lipschitz boundary.
In: Radu F., Kumar K., Berre I., Nordbotten J., Pop I. (eds),
Numerical Mathematics and Advanced Applications ENUMATH 2017.
Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham,
with Pietro Zanotti.
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Best error localizations for piecewise polynomial approximation of gradients, functions and functionals.
In: Radu F., Kumar K., Berre I., Nordbotten J., Pop I. (eds),
Numerical Mathematics and Advanced Applications ENUMATH 2017.
Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham.
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Quasi-optimality constants for parabolic Galerkin approximation in space.
In: Numerical Mathematics and Advanced Applications ENUMATH 2015.
Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham,
with Francesca Tantardini.
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Basic convergence results for conforming adaptive finite elements.
PAMM 7 (2008), 1026001-1026002,
with Pedro Morin and Kunibert G. Siebert.
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Convergence of finite elements adapted for weaker norms.
Applied and industrial mathematics in Italy II
(Selected papers from the 8th SIMAI Conference held in Ragusa, May 22-26, 2006),
468-470, Ser. Adv. Math. Appl. Sci. 75, World Sci. Publ., Hackensackm NJ, 2007,
with Pedro Morin and Kunibert G. Siebert.
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A safeguarded Zienkiewicz-Zhu estimator.
Numerical Mathematics and Advanced Applications.
Proceedings of ENUMATH 2005,
the 6th European Conference on Numerical Mathematics and Advanced Applications (Santiago de Compostela, 2005),
Springer Berlin, 269-276, 2006,
with Francesca Fierro.
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On a Posteriori Error Estimation for Constant Obstacle Problems.
Numerical methods for viscosity solutions and applications (Heraklion, 1999),
221-234, Ser. Adv. Math. Appl. Sci., 59, World Sci. Publishing, River Edge, NJ, 2001.
- Fehlerabschätzungen für ein Verfahren zur
Berechnung von zweidimensionalen Dendriten. Dissertation,
Mathematische Fakultät, Albert-Ludwigs-Universität
Freiburg im Breisgau (Germany), April 1998. Advisor:
Gerhard Dziuk.
Master's thesis
- Globale Existenz von Graphen unter inhomogenem
Krümmungsfluß bei Dirichlet-Randbedingungen.
Diplomarbeit, Institut für Angewandte Mathematik,
Albert-Ludwigs-Universität Freiburg im Breisgau (Germany),
December 1993. Advisor: Gerhard Dziuk.
Past
Last update: 07/09/2025 -- A. Veeser