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

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journal contribution
posted on 11.11.2016, 15:23 by Andrea Cangiani, Emmanuil H. Georgoulis, M. Jensen
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.

History

Citation

Applied Numerical Mathematics, 2016, 104, pp. 3-14 (12)

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Source

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

Version

AM (Accepted Manuscript)

Published in

Applied Numerical Mathematics

Publisher

Elsevier for International Association for Mathematics and Computers in Simulation (IMACS), North-Holland Publishing

issn

0168-9274

eissn

1873-5460

Available date

11/11/2016

Publisher version

http://www.sciencedirect.com/science/article/pii/S0168927414001081

Language

en