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Error bounds for POD expansions of parameterized transient temperatures

机译:参数化瞬态温度的POD扩展的误差范围

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We focus on the convergence analysis of the POD expansion for the parameterized solution of transient heat equations. The parameter of interest is the conductivity coefficient. We prove that this expansion converges with exponential accuracy, uniformly if the conductivity coefficient remains within a compact set of positive numbers. This convergence result is independent of the regularity of the temperature with respect to the space and time variables. We present some numerical experiments to show that a reduced number of modes allows to represent with high accuracy the family of solutions corresponding to parameters that lie in the compact set under study. (C) 2016 Elsevier B.V. All rights reserved.
机译:我们专注于瞬态热方程参数化解的POD展开的收敛性分析。感兴趣的参数是电导率系数。我们证明,如果电导系数保持在紧凑的正数范围内,则该扩展以指数精度收敛。该收敛结果与温度相对于空间和时间变量的规律性无关。我们提供了一些数值实验,以表明减少的模式数量可以高精度表示与研究中的紧凑集中的参数相对应的解决方案系列。 (C)2016 Elsevier B.V.保留所有权利。

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