In this talk, a multidimensional, multiphysics, two-phase transport model of proton exchange membrane fuel cell (PEMFC), which is based on the multiphase mixture formulation and encompasses all components in a PEMFC using a single computational domain, is specifically presented and simulated by a combined finite element-upwind finite volume method together with Newton's linearization, where flow, species, charge-transport and energy equations are simultaneously solved. To investigate the essential fuel cell model, I begin with a 2D simplified single-component two-phase PEFC model. Numerical simulations in 3D are carried out as well to explore and design efficient and robust numerical algorithms for the sake of fast and convergent nonlinear iteration. A more reasonable source term for water transport equation is given, and a series of efficient numerical algorithms and discretizations are designed and analyzed to achieve this goal. Our numerical simulations show that the convergent physical solutions can be reached within one hundred more steps, against the standard finite-volume based commercial CFD solvers which always produce oscillating iterations and never reach convergent solutions. Attained reasonable and comparable numerical solutions illustrate that our numerical methods and iterative algorithms are efficient and robust.