Regularization and discretization of inverse problems for PDEs in Banach spaces

• Applicants: Professor Dr. Christian Clason; Professor Dr. Daniel Wachsmuth
• Subject Area: Mathematics
• Term: from 2015 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 276832539

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.

• DFG Programme: Research Grants
• International Connection: Austria
• Partner Organisation: Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
• Cooperation Partner: Professorin Dr. Barbara Kaltenbacher