Space-time finite element methods for inverse problems

Dr. Huidong Yang

March 9, 2021, 3:30 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.