Space-time finite element methods for the initial temperature reconstruction
Abstract
This work is devoted to the reconstruction of the initial temperature in the backward heat equation using the 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 for an parabolic equation in the space-time domain. In this setting, the control is taken as initial condition, whereas the terminal observation data serve as target. The objective becomes a standard terminal observation functional combined with the Tikhonov regularization. The space-time finite element method is applied to the space-time optimality system that is well-posed for a fixed regularization parameter.
Keywords
Cite
@article{arxiv.2103.16699,
title = {Space-time finite element methods for the initial temperature reconstruction},
author = {Ulrich Langer and Olaf Steinbach and Fredi Tröltzsch and Huidong Yang},
journal= {arXiv preprint arXiv:2103.16699},
year = {2021}
}