  We developed a reduced order model (ROM) using the proper orthogonal
decomposition (POD) to compute efficiently the labyrinth and spot like patterns
of the FitzHugh-Nagumo (FNH) equation. The FHN equation is discretized in space
by the discontinuous Galerkin (dG) method and in time by the backward Euler
method. Applying POD-DEIM (discrete empirical interpolation method) to the full
order model (FOM) for different values of the parameter in the bistable
nonlinearity, we show that using few POD and DEIM modes, the patterns can be
computed accurately. Due to the local nature of the dG discretization, the
POD-DEIM requires less number of connected nodes than continuous finite element
for the nonlinear terms, which leads to a significant reduction of the
computational cost for dG POD-DEIM.
