A new error bound for Reduced Basis approximation of parabolic partial differential equations
نویسندگان
چکیده
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 βδ: βδ is bounded from below by unity for the heat equation; βδ grows only linearly in time for non-coercive (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 exponentially growing energy estimates.
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