A space-time certified reduced basis method for Burgers' equation
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...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
World Scientific
2015
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| Online Access: | http://hdl.handle.net/1721.1/97700 https://orcid.org/0000-0002-8323-9054 https://orcid.org/0000-0002-2631-6463 |
| Summary: | 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. |
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