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FORSCHUNGSBERICHT 1999-2001

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Institut für Angewandte Mathematik, Abt. f. Funktionalanalysis u. Numerische Mathematik

Allgemeine Angaben:
Wegelerstraße 6, 53115 Bonn
Telefon: 0228 / 73-3424
Fax: 0228 / 73-4698
eMail: kati@iam.uni-bonn.de
WWW: http://www.iam.uni-bonn.de

Hauptamtliche Professoren:
Prof. Dr. Hans-Wilhelm Alt
Prof. Dr. Angela Kunoth (seit 11.10.1999)
Prof. Dr. Martin Rumpf (bis 28.02.2001)
Prof. Dr. Karl Scherer

Wissenschaftliches Personal:
Universitätsstellen
Priv.-Doz. Herbert Arndt
Dr. Hans-Josef Bünger (verstorben am 14.10.2001)
Dr. Harald Garcke
Dipl.-Math. Karl-Wilhlem Jacobs
ADir. Dr. Paul Janßen
Dr. Barbara Niethammer
AOR Dr. Walter Pollul
Prof. Dr. Ing. Heinz Unger (em.)
Dipl.-Math. Peer Wasser (bis 31.12.2000)

Drittmittelstellen
Dipl.-Phys Carsten Burstedde (SFB 256)
Dipl.-Phys. Daniel Castano Diez (SFB 256)
Dipl.-Math. Armin Dahr (SFB 256)
Dipl.-Math. Martin Metscher (SFB 256)
Dipl.-Math. Matthias Roeger (SFB 256)
Dipl.-Math. Robert Strzodka (SFB 256)
Dipl.-Math. Sandra Wieland (SFB 256)
Dipl.-Math. Olga Wilderotter (SFB 256)

Forschungsschwerpunkte:
Parabolische Differentialgleichungen
(Alt)

Phasenübergänge
(Alt, Niethammer)

Probleme mit freiem Rand
(Alt, Niethammer)

Degeneriert parabolische Differentialgleichungen
(Garcke)

Geometrische Evolutionsgleichungen
(Garcke)

Mathematische Modelle zur Beschreibung von Phasenübergängen und Visualisierung
(Garcke)

Probleme mit freiem Rand
(Garcke)

Kontrollprobleme
(Kunoth)

Numerische Analysis, Wavelets
(Kunoth)

Kinetische Gleichungen
(Niethammer)

Computer Aided Design
(Scherer)

Splinefunktionen
(Scherer)

Wavelets
(Scherer)

Approximationstheorie
(Scherer, Pollul)

Besondere Forschungsförderung:
Analysis, modelling and simulation of multi-scale, multi-phase solidification in alloy systems
(Garcke, DFG im Rahmen des Schwerpunktprogramms Mehrskalenprobleme)

Homogenization of dilute particle dispersions
(Niethammer, DFG durch SPP Analysis, Modellierung und Numerik von Mehrskalenproblemen)

Multiple scales in phase separating systems with elastic misfit
(Garcke, Niethammer, Rumpf, Weikard, DFG durch SPP Analysis, Modellierung und Numerik von Mehrskalenproblemen)

Nonlinear Parabolic Partial Differential Equations
(Garcke, TMR)

Phasenfeldmodellierung der Erstarrung in mehrkomponentigen und mehrphasigen Legierungssystemen
(Garcke, DFG im Rahmen des Schwerpunktprogramms Phasenumwandlungen in mehrkomponentigen Schmelzen)

SFB 350 - C5 Geometrische Rekonstruktion und Simulation der Entwicklung von Schraegschichtungsgefuegen
(Kunoth, Castano, DFG)

Wavelets in Numerical Simulation
(Kunoth, EU-TMR)

Veröffentlichungen:

Barrett J W, Blowey J F, Garcke H
Finite element approximation of the Cahn-Hilliard equation with degenerate mobility
SIAM J. Num. Anal., Vol 37, No.1, 286-318, (1999)

Barrett J W, Blowey J F, Garcke H
On fully practical finite element approximations of degenerate Cahn-Hilliard systems
Math. Model. Num. Anal. (M2AN), Vol. 35 No. 4, 713--748, (2001)

Bertoluzza S, Kunoth A
Wavelet stabilization and preconditioning for domain decomposition
IMA J. Numer. Anal. 20 (2000), 533--559

Dahmen W, Han B, Jia R.-Q., Kunoth A
Biorthogonal multiwavelets on the interval: Cubic Hermite splines
Constr. Approx. 16 (2000), 221-259

Dahmen W, Kunoth A
Appending boundary conditions by Lagrange multipliers: Analysis of the LBB condition
Numer. Math. 88 (2001), 9-42.

Dahmen W , Kunoth A , Urban K
Biorthogonal spline-wavelets on the interval - Stability and moment conditions
Appl. Comput. Harm. Anal. 6 (1999), 132--196.

Dal Passo R, Garcke H
Solutions of a fourth order degenerate parabolic equation with weak initial trace
Ann. Scuola Normale Superiore Pisa Cl. (4), Vol. 28, No. 1, 153-181, (1999)

Garcke H, Nestler B
A mathematical model for grain growth in thin metallic films
Math. Models and Methods in Applied Sciences, Vol. 10, No. 6, 895-921, (2000)

Garcke H, Nestler B, Stoth B
A multi phase field concept: numerical simulations of moving phase boundaries and multiple junctions
SIAM J. Appl. Math., Vol. 60, No.1, 295-315, (1999)

Garcke H, Nestler B, Stoth B
Anisotropy in multiphase sytems: a phase-field approach
Interfaces and Free Boundaries, Vol. 1, No. 2, 175-198, (1999)

Garcke H, Novick-Cohen A
A singular limit for a system of degenerate Cahn-Hilliard equations
Adv. in Diff. Equations, 5, No. 4-6, 401-434, (2000)

Garcke H, Preußer T, Rumpf M, Telea A, Weikard U, van Wijk J
A Phase field model for continuous clustering on vector fields (ps.gz) (pdf)
IEEE Transactions on Visualization and Computer Graphics (TVCG), 7, 230--241, (2001)

Garcke H, Rumpf M, Weikard U
The Cahn-Hilliard equation with elasticity: Finite element approximation and qualitative studies
Interfaces and Free Boundaries, 3, 101--118, (2001)

Garroni A, Niethammer B
Correctors and error estimates in the homogenization of a Mullins-Sekerka problem
Ann. Inst. Henri Poincare, Anal. Non Lineaire 19 4 (2002), 371-393

Kohn RV, Niethammer B
Geometrically nonlinear shape-memory polycrystals made from a two-variant material
Math. Model. Num. Anal. (M2AN), 34 2 (2000), 377-398

Kunoth A
Wavelet Methods - Elliptic Boundary Value Problems and Control Problems
Teubner Verlag, 2001

Kunoth A
Wavelet techniques for the fictitious domain---Lagrange multiplier approach
Numer. Algor. 27 (2001), 291-316.

Lyche T, Scherer K
On the 1-norm condition number of the univariate Bernstein basis
Preprint , Bonn 2000, 26 pages (erscheint in Constr. Approximation)

Lyche T, Scherer K
On the p-norm Condition Number of the Multivariate Triangular Bernstein Basis
Journal Computational and Applied Mathematics 119 (2000), 259-273

Niethammer B
Derivation of the LSW-Theory for Ostwald Ripening by Homogenization Methods
Arch. Rat. Mech. Anal., 147 (1999) 2, 119-178

Niethammer B
The LSW--model for Ostwald Ripening with kinetic undercooling
Proc. Roy. Soc. Edinb., 130 A (2000), 1337-1361

Niethammer B, Otto F
Domain coarsening in thin films
Comm. Pure Appl. Math., 54 3 (2001), 361-384

Niethammer B, Otto F
Ostwald Ripening: The screening length revisited
Calc. Var., 13 1 (2001), 33-68

Niethammer B, Pego RL
Non-self-similar behavior in the LSW theory of Ostwald Ripening
J. Stat. Phys., 95 5/6 (1999), 867-902

Niethammer B, Pego RL
On the initial-value problem in the Lifshitz-Slyozov-Wagner theory of Ostwald Ripening
SIAM J. Math. Anal., 31 3 (2000), 467-485

Niethammer B, Pego RL
The LSW-model for domain coarsening: Asymptotic behavior fortotal conserved mass
J. Stat. Phys., 104 5/6 (2001),1113-1144

Scherer K
Parametric polynomial curves of local approximation order 8
Curves and Surface Fitting, Vanderbilt University Press, 2001, 375-384

Scherer K
Lower bounds for Bernstein -Bezier condition number
Mathematical Methods for Curves and Surfaces, Vanderbilt University Press, 2001, 433-443

Scherer K, Shadrin A Yu
New upper bounds for the B-spline basis condition number. A proof of deBoor's 2 k-conjecture
J. Approx. Theory 99 (1999), 217-229


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