Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolicPDEs are examined. The schemes under consideration are discontinuous in time butconforming in space and of arbitrary order. Stability estimates are presented in thenatural energy norms and at arbitrary times, under minimal regularity assumptions.Space-time error estimates of arbitrary order are derived, provided that the naturalparabolic regularity is present. Various physical parameters appearing in the model aretracked and numerical examples are presented.
