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A posteriori error estimation and space-time adaptivity for a linear stochastic PDE with additive noise
IMA Journal of Numerical Analysis ( IF 2.1 ) Pub Date : 2021-03-04 , DOI: 10.1093/imanum/drab013
Ananta K Majee 1 , Andreas Prohl 2
Affiliation  

We present a strong residual-based a posteriori error estimate for a finite element-based space-time discretization of the linear stochastic convected heat equation with additive noise. This error estimate is used for an adaptive algorithm that automatically selects deterministic mesh parameters in space and time. For every $n \geq 0$, we find a new time-step $\tau _n$, a new spatial mesh ${\mathcal M}_{n}$ terminating within finitely many iterations and a finite element value approximation $Y^n_h$ on this spatial mesh, which then approximates strongly the solution of the stochastic partial differential equation (SPDE) within a prescribed tolerance.

中文翻译:

具有加性噪声的线性随机偏微分方程的后验误差估计和时空自适应性

我们提出了基于有限元的时空离散化线性随机对流热方程与加性噪声的强残差后验误差估计。该误差估计用于自动选择空间和时间确定性网格参数的自适应算法。对于每个 $n \geq 0$,我们找到一个新的时间步长 $\tau _n$、一个在有限多次迭代内终止的新空间网格 ${\mathcal M}_{n}$ 和一个有限元值近似 $Y ^n_h$ 在这个空间网格上,然后在规定的容差内强烈逼近随机偏微分方程 (SPDE) 的解。
更新日期:2021-03-04
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