Heterogeneous conductivity parameters in a one dimensional fuel cell model

A model of one dimensional fuel cells is investigated, where the material inhomogeneities in the cathode are taken into account. We use the results in some preceding studies to describe the dynamics of the chemical reactions and transport of ions. A corresponding governing equation is derived for the numerical simulations. We apply an explicit-implicit time integration and Richardson extrapolation technique to increase the accuracy of the approximations. The efficiency of the method is demonstrated using a non-trivial test problem with real parameters. Numerical simulations are executed in presence of inhomogeneous conductivities and their effect on the cell potential is investigated

Stability concepts and their applications

The stability is one of the most basic requirement for the numerical model, which is mostly elaborated for the linear problems. In this paper we analyze the stability notions for the nonlinear problems. We show that, in case of consistency, both the N-stability and K-stability notions guarantee the convergence. Moreover, by using the N-stability we prove the convergence of the centralized Crank-Nicolson-method for the periodic initial-value transport equation. The K-stability is applied for the investigation of the forward Euler method and the θ-method for the Cauchy problem with Lipschitzian right side. © 2014 Elsevier Ltd. All rights reserved

On continuous and discrete maximum/minimum principles for reaction-diffusion problems with the Neumann boundary condition

summary:In this work, we present and discuss continuous and discrete maximum/minimum principles for reaction-diffusion problems with the Neumann boundary condition solved by the finite element and finite difference methods