Discontinuous Galerkin methods for convection-diffusion problems modelling mass-transfer through semipermeable membranes

We propose a family of Interior Penalty Discontinuous Galerkin (IP-DG) Finite element methods for the solution of semilinear convection-reaction-diffusion systems on partitioned subdomains arising in the modelling of mass transfer through semi-permeable membranes. Non-linear interface conditions are imposed at the sub-domain interfaces. The problem considered is relevant to the modelling of chemical species passing through thin biological membranes. In particular, we consider applications in cellular signal transduction. A series of numerical experiments highlight the good stability and accuracy properties of the proposed method.