Local Equilibration Error Estimators for Guaranteed Error Control in Adaptive Stochastic Higher-Order Galerkin Finite Element Methods
Local Equilibration Error Estimators for Guaranteed Error Control in Adaptive Stochastic Higher-Order Galerkin Finite Element Methods
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DOI：
10.1137/15m102188x
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发表时间：
2016-12
期刊：
影响因子：
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通讯作者：
M. Eigel;C. Merdon
中科院分区：
文献类型：
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作者：
M. Eigel;C. Merdon
在二阶椭圆型方程有限元法的后验误差控制中，平衡误差估计器通常可以得到非常精确的保证误差界。在这里，我们重新平衡通量高阶有限元与非常数系数，并说明了在两个确定性的基准设置的误差估计的不同变体的良好性能。在分别介绍了随机系数的参数问题和随机Galerkin有限元离散化后，设计了一种新的能量范数随机误差的后验误差估计。它是基于随机残差及其分解为近似残差和截断误差的随机离散化由于减少到一个有限的一组（随机）参数。重要的是，通过使用推导出的确定性平衡技术的近似残差，可计算的误差界是保证…
Equilibration error estimators have been shown to commonly lead to very accurate guaranteed error bounds in the a posteriori error control of finite element methods (FEMs) for second order elliptic equations. Here, we revisit equilibrated fluxes for higher-order FEMs with nonconstant coefficients and illustrate the favorable performance of different variants of the error estimator within two deterministic benchmark settings. After the introduction of the respective parametric problem with stochastic coefficients and the stochastic Galerkin FEM discretization, a novel a posteriori error estimator for the stochastic error in the energy norm is devised. It is based on the stochastic residual and its decomposition into approximation residuals and a truncation error of the stochastic discretization due to the reduction to a finite set of (random) parameters. Importantly, by using the derived deterministic equilibration techniques for the approximation residuals, the computable error bound is guaranteed for the...