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In cardiac electrophysiology, the propagation of the action potential may be described by a set of reaction–diffusion equations known as the bidomain model. The shape of the solution is determined by a balance of a strong reaction and a relatively weak diffusion, which leads to steep variations in space and time. From a numerical point of view, the sharp spatial gradients may be seen as particularly problematic, because computational grid resolution on the order of 0.1 mm or less is required, yielding considerable computational efforts on human geometries. In this paper, we discuss a number of well‐known numerical schemes for the bidomain equation and show how the quality of the solution is affected by the spatial discretization. In particular, we study in detail the effect of discretization on the conduction velocity (CV), which is an important quantity from a physiological point of view. We show that commonly …