A space-time certified reduced basis method for Burgers' equation

• Main Authors: Yano, Masayuki (Contributor), Patera, Anthony T. (Contributor), Urban, Karsten (Author)
• Other Authors: Massachusetts Institute of Technology. Department of Mechanical Engineering (Contributor)
• Format: Article
• Language: English
• Published: World Scientific, 2015-07-07T16:33:14Z.
• Subjects: Article
• Online Access: Get fulltext

 We present a space-time interpolation-based certified reduced basis method for Burgers' equation over the spatial interval (0, 1) and the temporal interval (0, T] parametrized with respect to the Peclet number. We first introduce a Petrov-Galerkin space-time finite element discretization which enjoys a favorable inf-sup constant that decreases slowly with Peclet number and final time T. We then consider an hp interpolation-based space-time reduced basis approximation and associated Brezzi-Rappaz-Raviart a posteriori error bounds. We describe computational offline-online decomposition procedures for the three key ingredients of the error bounds: the dual norm of the residual, a lower bound for the inf-sup constant, and the space-time Sobolev embedding constant. Numerical results demonstrate that our space-time formulation provides improved stability constants compared to classical L[superscript 2]-error estimates; the error bounds remain sharp over a wide range of Peclet numbers and long integration times T, in marked contrast to the exponentially growing estimate of the classical formulation for high Peclet number cases.