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 beta(delta): beta(delta) is unity for the heat equation; beta(delta) grows only linearly in time for non-coercive (but asymptotically stable) convection operators. The latter in turn permits effective long-time alpha posteriori error bounds for reduced basis approximations, in sharp contrast to classical (pessimistic) exponentially growing energy estimates. (C) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.