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arXiv · 2103.16699

Space-time finite element methods for the initial temperature reconstruction

Ulrich Langer·Olaf Steinbach·Fredi Tröltzsch·Huidong Yang
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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.

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Ulrich Langer, Olaf Steinbach, Fredi Tröltzsch, Huidong Yang. 2021-03-30. Space-time finite element methods for the initial temperature reconstruction. https://arxiv.org/abs/2103.16699

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