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

作者：Urban Karsten^*; Patera Anthony T

来源：Comptes Rendus Mathematique, 2012, 350(3-4): 203-207.

DOI：10.1016/j.crma.2012.01.026

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.

• 出版日期2012-2