Bradji, A. and Lesnic, D. orcid.org/0000-0003-3025-2770 (Cover date: September-October 2023) Steady-state inhomogeneous diffusion with generalized oblique boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis, 57 (5). pp. 2701-2733. ISSN 2822-7840
Abstract
We consider the elliptic diffusion (steady-state heat conduction) equation with space dependent conductivity and inhomogeneous source subject to a generalized oblique boundary condition on a part of the boundary and Dirichlet or Neumann boundary conditions on the remaining part. The oblique boundary condition represents a linear combination between the dependent variable and its normal and tangential derivatives at the boundary. We first prove the well-posedness of the continuous problems. We then develop new finite volume schemes for these problems and prove rigorously the stability and convergence of these schemes.We also address an application to the inverse corrosion problem concerning the reconstruction of the coefficients present in the generalized oblique boundary condition that is prescribed over a portion Γ0 of the boundary ∂Ω from Cauchy data on the complementary portion Γ1 = ∂Ω\Γ0.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The authors. Published by EDP Sciences, SMAI 2023 This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Oblique boundary condition, finite volume scheme, corrosion |
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: | 22 Sep 2023 15:32 |
Last Modified: | 22 Sep 2023 15:33 |
Published Version: | https://www.esaim-m2an.org/articles/m2an/abs/2023/... |
Status: | Published |
Publisher: | EDP Sciences |
Identification Number: | 10.1051/m2an/2023063 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:202039 |
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