| Issue |
ESAIM: M2AN
Volume 57, Number 5, September-October 2023
|
|
|---|---|---|
| Page(s) | 2701 - 2733 | |
| DOI | https://doi.org/10.1051/m2an/2023063 | |
| Published online | 14 September 2023 | |
Steady-state inhomogeneous diffusion with generalized oblique boundary conditions
1
LMA Laboratory, Faculty of Sciences, Badji Mokhtar-Annaba University, Annaba 23000, Algeria
2
University of Leeds, Department of Applied Mathematics, Leeds LS2 9JT, UK
* Corresponding author: d.lesnic@leeds.ac.uk
Received:
28
August
2022
Accepted:
24
July
2023
We consider the elliptic diffusion (steady-state heat conduction) equation with spacedependent 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.
Mathematics Subject Classification: 65M08 / 65M12 / 35J05
Key words: Oblique boundary condition / finite volume scheme / corrosion
© The authors. Published by EDP Sciences, SMAI 2023
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