Abstract

Diffusion coefficient identification from internal data represents one classical inverse problem for PDEs. Several different approaches have been proposed for their numerical recovery, however, a complete numerical analysis of these approaches is often missing due to the inherent nonlinearity of the direct problem. In this talk we present some a priori error estimates for the discrete minimizers obtained using regularized output least-squares formulation, one of the most classical approaches. I will discuss the main idea of analysis using conditional stability estimates for both elliptic and parabolic cases, and present numerical illustrations.

Bangti Jin received the Ph.D. degree in applied mathematics from the Chinese University of Hong Kong, Hong Kong, in 2008. Previously, he was a lecturer, reader and professor of Inverse problems at Department of Computer Science, University College London, London (2014-2022). an Assistant Professor of mathematics at the University of California, Riverside (2013–2014), a Visiting Assistant Professor at Texas A&M University (2010–2013), an Alexandre von Humboldt Postdoctoral Researcher at the University of Bremen (2009–2010). He is currently Professor of Mathematics at the Department of Mathematics, The Chinese University of Hong Kong His research interests include computational inverse problems, numerical analysis of differential equations, and machine learning.