A discrete de Rham discretization of interface diffusion problems with application to the Leaky Dielectric Model
<|reference_start|>A discrete de Rham discretization of interface diffusion problems with application to the Leaky Dielectric Model: 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.<|reference_end|>
@article{di pietro2024a,
    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},
    archivePrefix={arXiv},
    eprint={2409.15042},
    primaryClass={math.NA cs.NA}
}