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Title: Discontinuous Galerkin Methods for Mass Transfer through Semi-Permeable Membranes
Authors: Cangiani, Andrea
Georgoulis, Emmanuil H.
Jensen, Max
First Published: 30-Oct-2013
Publisher: Society for Industrial and Applied Mathematics (SIAM)
Citation: SIAM Journal on Numerical Analysis, 51 (5), pp. 2911–2934
Abstract: A discontinuous Galerkin (dG) method for the numerical solution of initial/boundary value multi-compartment partial differential equation (PDE) models, interconnected with interface conditions, is presented and analysed. The study of interface problems is motivated by models of mass transfer of solutes through semi-permeable membranes. More specifically, a model problem consisting of a system of semilinear parabolic advection-diffusion-reaction partial differential equations in each compartment, equipped with respective initial and boundary conditions, is considered. Nonlinear interface conditions modelling selective permeability, congestion and partial reflection are applied to the compartment interfaces. An interior penalty dG method is presented for this problem and it is analysed in the space-discrete setting. The a priori analysis shows that the method yields optimal a priori bounds, provided the exact solution is sufficiently smooth. Numerical experiments indicate agreement with the theoretical bounds and highlight the stability of the numerical method in the advection-dominated regime.
DOI Link: 10.1137/120890429
ISSN: 0036-1429
eISSN: 1095-7170
Version: Post-print and Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2013, Society for Industrial and Applied Mathematics. Deposited with reference to the publisher’s archiving policy available on the SHERPA/RoMEO website.
Appears in Collections:Published Articles, Dept. of Mathematics

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