Regularization and discretization of inverse problems for PDEs in Banach spaces

The aim of this project is a combined analysis of regularization and discretization of ill-posed problems in Banach spaces specifically in the context of partial differential equations. Such problems play a crucial role in numerous applications ranging from medical imaging via nondestructive testing to geophysical prospecting, with the Banach space setting mandated by the inherent regularity of the sought coefficients as well as structural features such as sparsity. Our goal is to fill the gap between the existing abstract regularization theory in general Banach spaces and the adaptive discretization of well-posed optimization problems in Hilbert spaces with pointwise constraints to derive explicit source conditions and practical parameter choice rules and to develop adaptive discretization methods based on functional and goal-oriented error estimates that take into account the interdependence of regularization parameter, data noise level and discretization error. This will lead to an integrated approach for the stable and efficient numerical solution method of parameter identification problems in Banach spaces.

Schlagworte: parameter identification, inverse problems, partial differential equations, regularization, discretization
Kurztitel: Inverse problems in Banach spaces
Zeitraum: 01.03.2016 - 31.08.2019
Homepage: -



Projekttyp Forschungsförderung (auf Antrag oder Ausschreibung)
Förderungstyp §26
  • Grundlagenforschung
  • Angewandte Forschung
  • 101002 - Analysis
  • 101014 - Numerische Mathematik
Forschungscluster Kein Forschungscluster ausgewählt
Genderrelevanz 0%
  • Science to Science (Qualitätsindikator: I)
Klassifikationsraster der zugeordneten Organisationseinheiten:
Arbeitsgruppen Keine Arbeitsgruppe ausgewählt


Organisation Adresse
Texas A&M University
400 Bizzell St
TX 77843 College Station
Vereinigte St. v. Amerika
400 Bizzell St
US - TX 77843  College Station
Karl-Franzens-Universität Graz
Universitätsplatz 3
8010 Graz
Österreich - Steiermark
Universitätsplatz 3
AT - 8010  Graz
Universität Duisburg-Essen, Campus Essen
Universitätsstraße 2
45141 Essen
Universitätsstraße 2
DE - 45141  Essen
TU Chemnitz
Straße der Nationen 62
09111 Chemnitz
Straße der Nationen 62
DE - 09111  Chemnitz
Universität Hamburg
DE  Hamburg
Helmholtz Zentrum München
Ingolstädter Landstraße 1
85764 Neuherberg
Ingolstädter Landstraße 1
DE - 85764  Neuherberg
University of Würzburg
Sanderring 2
97070 Würzburg
Sanderring 2
DE - 97070  Würzburg