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A discrete de Rham discretization of interface diffusion problems with application to the Leaky Dielectric Model
- Publication Year :
- 2024
-
Abstract
- Motivated by the study of the electrodynamics of particles, we propose in this work an arbitrary-order discrete de Rham scheme for the treatment of elliptic problems with potential and flux jumps across a fixed interface. The scheme seamlessly supports general elements resulting from the cutting of a background mesh along the interface. Interface conditions are enforced weakly \`a la Nitsche. We provide a rigorous convergence of analysis of the scheme for a steady model problem and showcase an application to a physical problem inspired by the Leaky Dielectric Model.
- Subjects :
- Mathematics - Numerical Analysis
78M10, 65N30, 35J15
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2409.15042
- Document Type :
- Working Paper