A space-time hp-interpolation-based certified reduced basis method for Burgers' equation
A space-time hp-interpolation-based certified reduced basis method for Burgers' equation
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DOI：
10.1142/s0218202514500110
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发表时间：
2014-05
影响因子：
3.5
通讯作者：
M. Yano;A. Patera;K. Urban
中科院分区：
文献类型：
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作者：
M. Yano;A. Patera;K. Urban
提出了一种基于时空插值的保约基方法，求解空间（0，1）和时间（0，T]上的Burgers方程.我们首先介绍了一种Petrov-Galerkin时空有限元离散，它具有良好的inf-sup常数，随着Peclet数和最终时间T缓慢下降。然后，我们考虑基于hp插值的时空约化基近似和相关的Brezzi-Rappaz-Raviart后验误差界。我们描述了计算离线在线分解程序的误差界的三个关键成分：对偶范数的残差，下限的inf-sup常数，和空间-时间Sobolev嵌入常数。数值结果表明，我们的时空配方提供了改进的稳定常数相比，经典的L2-误差估计，误差界保持尖锐的范围广泛的Peclet数和长的积分时间T，在显着对比指数增长的估计经典配方高Peclet数的情况下。
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 L2-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.