Energy Norm A Posteriori Error Estimation for Parametric Operator Equations
Energy Norm A Posteriori Error Estimation for Parametric Operator Equations
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DOI：
10.1137/130916849
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发表时间：
2014-03
期刊：
影响因子：
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通讯作者：
A. Bespalov;C. Powell;D. Silvester
中科院分区：
文献类型：
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作者：
A. Bespalov;C. Powell;D. Silvester
随机Galerkin逼近是求解相关随机数据椭圆偏微分方程的一种常用方法。一个典型的策略是结合联合收割机传统的（$h$-）空间域上的有限元近似与（随机）参数域上的有限维流形上的谱（$p$-）近似。本文使用参数算子方程的抽象设置概述了计算解的后验误差分析中所涉及的问题。引入了一种新的能量误差估计器，它使用了基本微分算子的无参数部分，有效地利用了近似空间的张量积结构。我们证明了我们的误差估计器是可靠且有效的。我们还讨论了不同的策略，丰富的近似空间，并证明了双边估计的误差减少相应的增强近似。这些给出了可计算的估计的误差减少，只依赖于…
Stochastic Galerkin approximation is an increasingly popular approach for the solution of elliptic PDE problems with correlated random data. A typical strategy is to combine conventional ($h$-)finite element approximation on the spatial domain with spectral ($p$-)approximation on a finite-dimensional manifold in the (stochastic) parameter domain. The issues involved in a posteriori error analysis of computed solutions are outlined in this paper using an abstract setting of parametric operator equations. A novel energy error estimator that uses a parameter-free part of the underlying differential operator is introduced which effectively exploits the tensor product structure of the approximation space. We prove that our error estimator is reliable and efficient. We also discuss different strategies for enriching the approximation space and prove two-sided estimates of the error reduction for the corresponding enhanced approximations. These give computable estimates of the error reduction that depend only on...