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

Cangiani, Andrea, Georgoulis, Emmanuil H and Jensen, Max (2016) Discontinuous Galerkin methods for fast reactive mass transfer through semi-permeable membranes. Applied Numerical Mathematics, 104. pp. 3-14. ISSN 0168-9274

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Max Jensen
Date Deposited: 02 Jul 2014 07:25
Last Modified: 14 Mar 2017 22:14
URI: http://sro.sussex.ac.uk/id/eprint/49138

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