TY - JOUR
A1 - Harrach, Bastian von
T1 - Uniqueness, stability and global convergence for a discrete inverse elliptic Robin transmission problem
T2 - Numerische Mathematik
N2 - We derive a simple criterion that ensures uniqueness, Lipschitz stability and global convergence of Newtonâ€™s method for the finite dimensional zero-finding problem of a continuously differentiable, pointwise convex and monotonic function. Our criterion merely requires to evaluate the directional derivative of the forward function at finitely many evaluation points and for finitely many directions. We then demonstrate that this result can be used to prove uniqueness, stability and global convergence for an inverse coefficient problem with finitely many measurements. We consider the problem of determining an unknown inverse Robin transmission coefficient in an elliptic PDE. Using a relation to monotonicity and localized potentials techniques, we show that a piecewise-constant coefficient on an a-priori known partition with a-priori known bounds is uniquely determined by finitely many boundary measurements and that it can be uniquely and stably reconstructed by a globally convergent Newton iteration. We derive a constructive method to identify these boundary measurements, calculate the stability constant and give a numerical example.
Y1 - 2020
UR - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/63780
UR - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-637808
SN - 0945-3245
N1 - Open Access funding enabled and organized by Projekt DEAL.
VL - 147
IS - 1
SP - 29
EP - 70
PB - Springer
CY - Berlin ; Heidelberg
ER -