期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 24, 期 9, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202514500110
关键词
Space-time variational formulation; parametrized parabolic equations; quadratic non-linearity; reduced basis; Brezzi-Rappaz-Raviart theory; a posteriori error bounds; inf-sup constant; Burgers' equation
资金
- OSD/AFOSR/MURI [FA9550-09-1-0613]
- ONR [N00014-11-1-0713]
- Deutsche Forschungsgemeinschaft (DFG) [Ur-63/9, GrK1100]
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-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
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