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Title: Discontinuous Galerkin methods for fast reactive mass transfer through semi-permeable membranes
Authors: Cangiani, Andrea
Georgoulis, Emmanuil H.
Jensen, M.
First Published: 25-Jun-2014
Presented at: Fifth International Conference on Numerical Analysis – Recent Approaches to Numerical Analysis: Theory, Methods and Applications (NumAn 2012), held in Ioannina, Sixth International Conference on Numerical Analysis – Recent Approaches to Numerical Analysis: Theory, Methods and Applications (NumAn 2014), held in Chania, in memory of Theodore S. Papatheodorou
Publisher: Elsevier for International Association for Mathematics and Computers in Simulation (IMACS), North-Holland Publishing
Citation: Applied Numerical Mathematics, 2016, 104, pp. 3-14 (12)
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 analysed. The study of interface problems is motivated by models of mass transfer of solutes through semi-permeable membranes. The case of fast reactions is also included. More specifically, a model problem consisting of a system of semilinear parabolic advection–diffusion–reaction partial differential equations in each compartment with only local Lipschitz conditions on the nonlinear reaction terms, equipped with respective initial and boundary conditions, is considered. General nonlinear interface conditions modelling selective permeability, congestion and partial reflection are applied to the compartment interfaces. The interior penalty dG method for this problem, presented recently, is analysed both in the space-discrete and in fully discrete settings for the case of, possibly, fast reactions. 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.
DOI Link: 10.1016/j.apnum.2014.06.007
ISSN: 0168-9274
eISSN: 1873-5460
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Creative Commons “Attribution Non-Commercial No Derivatives” licence CC BY-NC-ND, further details of which can be found via the following link: Archived with reference to SHERPA/RoMEO and publisher website.
Appears in Collections:Published Articles, Dept. of Mathematics

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