Space-time finite element methods for inverse problems
Dr. Huidong YangMarch 9, 2021, 2:30 p.m. ZOOM
This work is devoted to the initial temperature reconstruction in the backward heat equation using a space-time finite element method on fully unstructured space-time simplicial meshes proposed by Steinbach (2015). Such a severely ill-posed problem is tackled by the standard Tikhonov
regularization method. This leads to a related optimal control of parabolic equations in the space-time domain. In this setting, the control is taken as initial condition, whereas the terminal observation data serves as target. The objective becomes a standard terminal observation functional combined with the Tikhonov regularization. The regularization parameter is successively defined by Morozov's discrepancy principle.