New Error Bound for Reduced Basis Approximation of Parabolic Partial Differential Equations

摘要

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 a posteriori error bounds for reduced basis approximations in sharp contrast to classical (pessimistic) exponentially growing energy estimates.