TY - JOUR
T1 - An iterative regularizing method for an incomplete boundary data problem for the biharmonic equation
AU - Chapko, Roman
AU - Johansson, B. Tomas
N1 - This is the peer reviewed version of the following article: Chapko R, Johansson BT. An iterative regularizing method for an incomplete boundary data problem for the biharmonic equation. Z Angew Math Mech. 2018;98:2010–2021, which has been published in final form at https://doi.org/10.1002/zamm.201800102. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
PY - 2018/11/1
Y1 - 2018/11/1
N2 - An incomplete boundary data problem for the biharmonic equation is considered, where the displacement is known throughout the boundary of the solution domain whilst the normal derivative and bending moment are specified on only a portion of the boundary. For this inverse ill‐posed problem an iterative regularizing method is proposed for the stable data reconstruction on the underspecified boundary part. Convergence is proven by showing that the method can be written as a Landweber‐type procedure for an operator formulation of the incomplete data problem. This reformulation renders a stopping rule, the discrepancy principle, for terminating the iterations in the case of noisy data. Uniqueness of a solution to the considered problem is also shown.
AB - An incomplete boundary data problem for the biharmonic equation is considered, where the displacement is known throughout the boundary of the solution domain whilst the normal derivative and bending moment are specified on only a portion of the boundary. For this inverse ill‐posed problem an iterative regularizing method is proposed for the stable data reconstruction on the underspecified boundary part. Convergence is proven by showing that the method can be written as a Landweber‐type procedure for an operator formulation of the incomplete data problem. This reformulation renders a stopping rule, the discrepancy principle, for terminating the iterations in the case of noisy data. Uniqueness of a solution to the considered problem is also shown.
UR - https://onlinelibrary.wiley.com/doi/abs/10.1002/zamm.201800102
U2 - 10.1002/zamm.201800102
DO - 10.1002/zamm.201800102
M3 - Article
SN - 0044-2267
VL - 98
SP - 2010
EP - 2021
JO - ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
JF - ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
IS - 11
ER -