Prof. Dr. Barbara Zwicknagl

Profil

Zusammenfassung

Barbara Zwicknagl entwickelt mathematische Methoden zur Analyse von Differentialgleichungen und Variationsproblemen, die in der Materialwissenschaft und Physik auftreten. Ihre Expertise umfasst die theoretische Untersuchung von Mikrostrukturen, Phasenübergängen und Musterbildung sowie die Entwicklung von Approximations- und Interpolationsmethoden. Diese Kompetenzen sind für Industrie relevant, die komplexe Materialverhalten modellieren und numerisch simulieren muss.

Skills

Name

Prof. Dr. Barbara Zwicknagl

Titel

Prof. Dr.

Fakultät

Mathematisch-Naturwissenschaftliche Fakultät

Institut

Institut für Mathematik

Arbeitsgruppe

Angewandte Analysis

E-Mail

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HU-FIS-Profil

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Zuletzt gescrapt

28.6.2026, 01:15:12

• Dynamic Phenomena in Elasticity Problems

  Quelle ↗

  Förderer: Volkswagen Stiftung Zeitraum: 06/2022 - 06/2023 Projektleitung: Prof. Dr. Barbara Zwicknagl

• From Modeling and Analysis to Approximation

  Quelle ↗

  Förderer: Volkswagen Stiftung Zeitraum: 01/2020 - 12/2023 Projektleitung: Prof. Dr. Barbara Zwicknagl

• Q13 - Variational models for pattern formation in biomembranes

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  Förderer: DFG Graduiertenkolleg Zeitraum: 10/2021 - 03/2023 Projektleitung: Prof. Dr. Barbara Zwicknagl

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• Sampling inequalities for infinitely smooth functions, with applications to interpolation and machine learning

  2008

  Advances in Computational Mathematics · 59 Zitationen · DOI

  Sampling inequalities give a precise formulation of the fact that a differentiable function cannot attain large values if its derivatives are bounded and if it is small on a sufficiently dense discrete set. Sampling inequalities can be applied to the difference of a function and its reconstruction in order to obtain (sometimes optimal) convergence orders for very general possibly regularized recovery processes. So far, there are only sampling inequalities for finitely smooth functions, which lead to algebraic convergence orders. In this paper, the case of infinitely smooth functions is investigated, in order to derive error estimates with exponential convergence orders.

• Power Series Kernels

  2008

  Constructive Approximation · 40 Zitationen · DOI

  We introduce a class of analytic positive definite multivariate kernels which includes infinite dot product kernels as sometimes used in machine learning, certain new nonlinearly factorizable kernels, and a kernel which is closely related to the Gaussian. Each such kernel reproduces in a certain “native” Hilbert space of multivariate analytic functions. If functions from this space are interpolated in scattered locations by translates of the kernel, we prove spectral convergence rates of the interpolants and all derivatives. By truncation of the power series of the kernel-based interpolants, we constructively generalize the classical Bernstein theorem concerning polynomial approximation of analytic functions to the multivariate case. An application to machine learning algorithms is presented.

• Microstructures in Low-Hysteresis Shape Memory Alloys: Scaling Regimes and Optimal Needle Shapes

  2014

  Archive for Rational Mechanics and Analysis · 36 Zitationen · DOI

• Baltische Föderale Immanuel-Kant-Universität

  From Modeling and Analysis to Approximation

  university

• Kharkiv National Universität

  Dynamic Phenomena in Elasticity Problems

  university

• National Academy of Sciences of Ukraine

  Dynamic Phenomena in Elasticity Problems

  university