Variational formulation with error estimates for uncertainty quantification via collocation, regression, and sprectral projection
Variational formulation with error estimates for uncertainty quantification via collocation, regression, and sprectral projection
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通过搭配、回归和谱投影进行不确定性量化的误差估计的变分公式
DOI：
10.1002/pamm.201710024
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
H. G. Matthies
中科院分区：
文献类型：
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作者：
J. Rang;H. G. Matthies
许多真实的世界问题需要简化，以减少计算来回答特定的问题，例如，量化不确定性。因此，基于插值或近似方法开发了所谓的元模型或代理模型。在本文中，我们通常的逼近或插值问题转化为变分形式，如它是已知的有限元法（FEM）。有了这个变分的框架，它是可能的，以获得误差估计，这可以用于以后的适应性。为了计算元模型的系数，需要一些求积规则，这些规则应该与给定的数据相关。一个数值例子显示了我们所提出的方法的优点。（© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA，魏因海姆）
Many real world problems need simplifications in such a way that computing is reduced for answering specific questions, for example, to quantify uncertainties. Therefore so‐called metamodels or surrogate models are developed which are based on interpolation or approximation methods. In this paper we transform the usual approximation or interpolation problem into a variational form such as it is known from the Finite Element method (FEM). With this variational framework it is possible to derive error estimators, which can be used later on for adaptivity. To compute the coefficients of the metamodel one needs some quadrature rules, which should be related to the given data. A numerical example shows the advantages of our proposed methods. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)