Year: 2025
Type: article
Abstract: Hybrid finite element methods, particularly hybridized discontinuous Galerkin methods, are efficient numerical schemes for discretizing the diffusion equation, which encompasses two main physical prin-ciples: mass conservation and positivity preservation. While the former has been extensively analysed in the literature, this paper investigates the latter. We state a theorem that guarantees the positivity of both the bulk and skeleton approximations to the primary unknown (concentration) and provide counterexamples for nonpositive discretizations. The theoretical findings are confirmed by numerical experiments.
Authors: Petr Knobloch, Philip L Lederer, Andreas Rupp
Institutions: Charles University, Universität Hamburg, Saarland University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: Uncertainty quantification for PDEs on hypergraphs, Mathematical theory and numerical analysis for equations of viscous newtonian compressible fluids, G33094125, Co-Innovation, tutkimusosallistuja — Lappeenrannan-Lahden teknillinen yliopisto LUT (539/31/2023), G7623643547, Flagship of Advanced Mathematics for Sensing, Imaging and Modelling
OpenAlex ID: W4417345520