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

2024/10/07 by Gabriel R. Barrenechea, Barrenechea, Gabriel R., Tristan Pryer +3 · 2 citations
Computer Science · Engineering · Mathematics · #2010: 65M60 (Primary) #65M22 (Secondary) #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2410.05040

openalex publication_date 2024/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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• A nodally bound-preserving composite discontinuous Galerkin method on polytopic meshes
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