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Mathematical modelling and numerical simulation are important tools for understanding and developing solid oxide fuel cell technology. An SOFC is a multi‐scale system, where processes on all time and length scales contribute to the observed macroscopic system behaviour. This review gives an overview of modelling techniques on all scales – atomistic, electrode, cell, stack, system – where each scale follows its own methodology and software. A particular focus is put on the bridging of scales, that is, the combination of modelling techniques from two or more adjacent scales. Comprehensive examples are given that illustrate the richness and diversity of today*s SOFC modelling community.

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