A new error bound for reduced basis approximation of parabolic partial differential equations

We consider a space–time variational formulation for linear parabolic partial differential equations. We introduce an associated Petrov–Galerkin truth finite element discretization with favorable discrete inf-sup constant β δ : β δ is unity for the heat equation; β δ grows only linearly in time for non-coercive (but asymptotically stable) convection operators. The latter in turn permits effective long-time a posteriori error bounds for reduced basis approximations, in sharp contrast to classical (pessimistic) exponentially growing energy estimates.