In this work, we study a surface reaction on Pd(111) crystals under ultra-high-vacuum conditions that can be modeled by two coupled reaction-diffusion equations. In the bistable regime, the reaction exhibits travelling fronts that can be observed experimentally using photo electron emission microscopy. The spatial profile of the fronts reveals a coverage-dependent diffusivity for one of the species. We propose a method to solve the nonlinear eigenvalue problem and compute the direction and the speed of the fronts based on a geometrical construction in phase-space. This method successfully captures the dependence of the speed on control parameters and diffusivities.