Nitsche extended finite element method of a Ventcel transmission problem with discontinuities at the interface
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.
Authors
- Daniela Capatina (ORCID: https://orcid.org/0009-0001-0380-0412)
- Marc Dambrine (ORCID: https://orcid.org/0000-0003-0173-9950)
- Fabien Caubet (ORCID: https://orcid.org/0000-0002-6379-3867)
- Rodrigo Zelada
Institutions
- Centre National de la Recherche Scientifique (FR)
- Université de Pau et des Pays de l'Adour (FR)
- Universidad Bernardo O'Higgins (CL)
- Laboratoire de Mathématiques et de leurs Applications (FR)
- University of Chile (CL)
Publication Details
- Journal
- ESAIM. Mathematical modelling and numerical analysis
- Published
- 2025-03-01
- DOI
- https://doi.org/10.1051/m2an/2025014
- Citations
- 3
- Primary Topic
- Contact Mechanics and Variational Inequalities
- Type
- article
- Field-Weighted Citation Impact
- 4.51
Funders
- Agenția Națională pentru Cercetare și Dezvoltare
- Agencia Nacional de Investigación y Desarrollo
- CHIST-ERA