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

• Main Authors: Urban, Karsten (Author), Patera, Anthony T. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Mechanical Engineering (Contributor)
• Format: Article
• Language: English
• Published: Elsevier, 2015-10-21T14:42:49Z.
• Subjects: Article
• Online Access: Get fulltext

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[subscript δ]:β[subscript δ] is unity for the heat equation; β[subscript 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.
United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550-09-1-0613)
United States. Office of Naval Research (Grant N00014-11-1-0713)