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

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posted on 2023-06-08, 17:41 authored by Andrea Cangiani, Emmanuil H Georgoulis, Max 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

Publication status

  • Published

File Version

  • Accepted version

Journal

Applied Numerical Mathematics

ISSN

0168-9274

Publisher

Elsevier

Volume

104

Page range

3-14

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2014-07-02

First Open Access (FOA) Date

2016-04-14

First Compliant Deposit (FCD) Date

2014-07-02

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