arXiv Open Access 2024

A nodally bound-preserving discontinuous Galerkin method for the drift-diffusion equation

Gabriel R. Barrenechea Tristan Pryer Alex Trenam
Lihat Sumber

Abstrak

In this work, we introduce and analyse discontinuous Galerkin (dG) methods for the drift-diffusion model. We explore two dG formulations: a classical interior penalty approach and a nodally bound-preserving method. Whilst the interior penalty method demonstrates well-posedness and convergence, it fails to guarantee non-negativity of the solution. To address this deficit, which is often important to ensure in applications, we employ a positivity-preserving method based on a convex subset formulation, ensuring the non-negativity of the solution at the Lagrange nodes. We validate our findings by summarising extensive numerical experiments, highlighting the novelty and effectiveness of our approach in handling the complexities of charge carrier transport.

Topik & Kata Kunci

Penulis (3)

G

Gabriel R. Barrenechea

T

Tristan Pryer

A

Alex Trenam

Format Sitasi

Barrenechea, G.R., Pryer, T., Trenam, A. (2024). A nodally bound-preserving discontinuous Galerkin method for the drift-diffusion equation. https://arxiv.org/abs/2410.05040

Akses Cepat

Lihat di Sumber
Informasi Jurnal
Tahun Terbit
2024
Bahasa
en
Sumber Database
arXiv
Akses
Open Access ✓