| Issue |
ESAIM: M2AN
Volume 59, Number 2, March-April 2025
|
|
|---|---|---|
| Page(s) | 999 - 1021 | |
| DOI | https://doi.org/10.1051/m2an/2025014 | |
| Published online | 02 April 2025 | |
Nitsche extended finite element method of a Ventcel transmission problem with discontinuities at the interface
Université de Pau et des Pays de l’Adour, E2S UPPA, CNRS, LMAP, UMR 5142, 64000 Pau, France
* Corresponding author: fabien.caubet@univ-pau.fr
Received:
24
May
2024
Accepted:
3
March
2025
The objective of this work is to study a diffusion equation with non-standard transmission conditions, which include discontinuities and Ventcel boundary conditions at the interface. In order to handle jumps and means of the flux and the test-functions, we use broken Sobolev spaces. We present a Nitsche type finite element approach and compare it with a discontinuous Galerkin method. We establish consistency, stability and a priori error estimates, and verify them numerically.
Mathematics Subject Classification: 65N12 / 65N15 / 65N30 / 35S15 / 35C20
Key words: Finite element method / Nitsche method / Ventcel boundary condition / asymptotic model
© The authors. Published by EDP Sciences, SMAI 2025
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