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Discontinuous Galerkin methods for fast reactive mass transfer through semi-permeable membranes

Cangiani, Andrea; Georgoulis, Emmanuil H; Jensen, Max; (2016) Discontinuous Galerkin methods for fast reactive mass transfer through semi-permeable membranes. Applied Numerical Mathematics , 104 pp. 3-14. 10.1016/j.apnum.2014.06.007. Green open access

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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

Type: Article
Title: Discontinuous Galerkin methods for fast reactive mass transfer through semi-permeable membranes
Location: Univ Ioannina, Ioannina, GREECE
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.apnum.2014.06.007
Publisher version: https://doi.org/10.1016/j.apnum.2014.06.007
Language: English
Additional information: This version is the author-accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Interface modelling, Mass transfer, Fast reactions, Discontinuous Galerkin methods, Semilinear parabolic problems, Nonlinear interface conditions
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10164366
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