A discrete de Rham discretization of interface diffusion problems with application to the Leaky Dielectric Model
Numerical Analysis
2024-09-24 v1 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2409.15042,
title = {A discrete de Rham discretization of interface diffusion problems with application to the Leaky Dielectric Model},
author = {Daniele A. Di Pietro and Simon Mendez and Aurelio Edoardo Spadotto},
journal= {arXiv preprint arXiv:2409.15042},
year = {2024}
}