Guaranteed, Locally Space-Time Efficient, and Polynomial-Degree Robust a Posteriori Error Estimates for High-Order Discretizations of Parabolic Problems
Guaranteed, Locally Space-Time Efficient, and Polynomial-Degree Robust a Posteriori Error Estimates for High-Order Discretizations of Parabolic Problems
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抛物型问题高阶离散化的有保证、局部时空有效、多项式鲁棒的后验误差估计
DOI：
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发表时间：
2016
影响因子：
2.9
通讯作者：
M. Vohralík
中科院分区：
文献类型：
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作者：
A. Ern;Iain Smears;M. Vohralík
我们考虑了基于任意高阶协调Galerkin空间离散和任意高阶不连续Galerkin时间离散的抛物问题的近似的后验误差分析。利用平衡通量重建，我们给出了误差的$L^2（H^1）帽H^1（H^{-1}）$-范数和数值解的时间跳跃组成的范数的后验误差估计.估计提供了保证上界，这个规范没有未知常数。此外，相对于这个规范的估计的效率在空间和时间上都是局部的，具有相对于网格大小、时间步长以及空间和时间多项式次数是鲁棒的常数。我们进一步证明了这个范数是局部时空效率的关键，它全局等价于误差的$L^2（H^1）cap H^1（H^{-1}）$-范数，具有多项式次数的鲁棒常数。建议的估计也有实际的优势是…
We consider the a posteriori error analysis of approximations of parabolic problems based on arbitrarily high-order conforming Galerkin spatial discretizations and arbitrarily high-order discontinuous Galerkin temporal discretizations. Using equilibrated flux reconstructions, we present a posteriori error estimates for a norm composed of the $L^2(H^1)cap H^1(H^{-1})$-norm of the error and the temporal jumps of the numerical solution. The estimators provide guaranteed upper bounds for this norm without unknown constants. Furthermore, the efficiency of the estimators with respect to this norm is local in both space and time, with constants that are robust with respect to the mesh-size, time-step size, and the spatial and temporal polynomial degrees. We further show that this norm, which is key for local space-time efficiency, is globally equivalent to the $L^2(H^1)cap H^1(H^{-1})$-norm of the error, with polynomial-degree robust constants. The proposed estimators also have the practical advantage of being...
等误差分布抛物线问题的收敛时空自适应dG(s)有限元方法
DOI：
10.1093/imanum/dry005
发表时间：
2019
期刊：
arXiv: Numerical Analysis
影响因子：
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作者：
F. D. Gaspoz;C. Kreuzer;K. G. Siebert;D. Ziegler
通讯作者：
D. Ziegler