Finite element approximation analysis for a steady state two-phase transport model of proton exchange membrane fuel cell

In this paper, we study a 2D steady state two‐phase transport model of water species which occurs in the cathode gas diffusion layer of proton exchange membrane fuel cell (PEMFC). The reformulation of water transport equation is described by Kirchhoff transformation to deal with the discontinuous and degenerate water diffusivity due to phase change. Finite element approximation is developed for the present model and the optimal error estimate in $H^1$ norm and the sub‐optimal error estimate in $L^2$ norm are obtained for the multiphase mixture model of PEMFC for the first time. Numerical experiments are also performed to verify the theoretical results.