Huntul, M and Lesnic, D orcid.org/0000-0003-3025-2770 (2021) Determination of the time-dependent convection coefficient in two-dimensional free boundary problems. Engineering Computations, 38 (10). pp. 3694-3709. ISSN 0264-4401
Abstract
Purpose:
The purpose of the study is to solve numerically the inverse problem of determining the time-dependent convection coefficient and the free boundary, along with the temperature in the two-dimensional convection-diffusion equation with initial and boundary conditions supplemented by non-local integral observations. From the literature, there is already known that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data.
Design/methodology:
For the numerical discretization, this paper applies the alternating direction explicit finite-difference method along with the Tikhonov regularization to find a stable and accurate numerical solution. The resulting nonlinear minimization problem is solved computationally using the MATLAB routine lsqnonlin. Both exact and numerically simulated noisy input data are inverted.
Findings:
The numerical results demonstrate that accurate and stable solutions are obtained.
Originality/value:
The inverse problem presented in this paper was already showed to be locally uniquely solvable, but no numerical solution has been realized so far; hence, the main originality of this work is to attempt this task.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021, Emerald Publishing Limited. This is an author produced version of an article published in Engineering Computations. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Free boundary; Heat equation; Inverse problem; Nonlinear optimization; Tikhonov regularization; Two-dimensional |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 20 Jan 2021 14:10 |
Last Modified: | 29 Jul 2022 11:32 |
Status: | Published |
Publisher: | Emerald |
Identification Number: | 10.1108/EC-10-2020-0562 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:169932 |