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Electrochemical systems are complicated, with Faradaic processes commonly coupled to chemical and adsorption/absorption reactions, and partially controlled by the diffusion of species in solution and/or the migration and diffusion of defects in solids. They become more complicated when radiation is involved. Quantitative kinetic analysis of such systems inevitably requires the modeling of experimental systems, involving the solutions of diffusion-reaction equations with appropriate boundary conditions that describe the system. We are modelling such systems and processes using the finite element method by application of the modelling package, COMSOL Multiphysics. These include (a) the development of acidity in pores and flaws in UO2 and deposits on UO2 under anodic conditions, (b) the determination of local corrosion kinetics on non-stoichiometric UO2+x, (c) the permeation of hydrogen through a thin TiO2 film, (d) the influence of steel corrosion products on nuclear fuel corrosion under permanent disposal conditions, (e) fuel corrosion within cracks on the surface of spent fuel pellets, and (f) (α, β, γ) radiolyses and their effects on corrosion of UO2, Tc, and Cu.