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Stochastic goal-oriented error estimation with memory

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Ackmann,  Jan
IMPRS on Earth System Modelling, MPI for Meteorology, Max Planck Society;
Applied Mathematics and Computational Physics (AMCP), Scientific Computing Lab (ScLab), MPI for Meteorology, Max Planck Society;

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Marotzke,  Jochem       
Director’s Research Group OES, The Ocean in the Earth System, MPI for Meteorology, Max Planck Society;

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Korn,  Peter
Applied Mathematics and Computational Physics (AMCP), Scientific Computing Lab (ScLab), MPI for Meteorology, Max Planck Society;

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Citation

Ackmann, J., Marotzke, J., & Korn, P. (2017). Stochastic goal-oriented error estimation with memory. Journal of Computational Physics, 348, 195-219. doi:10.1016/j.jcp.2017.07.009.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-D779-C
Abstract
We propose a stochastic dual-weighted error estimator for the viscous shallow-water equation with boundaries. For this purpose, previous work on memory-less stochastic dual-weighted error estimation is extended by incorporating memory effects. The memory is introduced by describing the local truncation error as a sum of time-correlated random variables. The random variables itself represent the temporal fluctuations in local truncation errors and are estimated from high-resolution information at near-initial times. The resulting error estimator is evaluated experimentally in two classical ocean-type experiments, the Munk gyre and the flow around an island. In these experiments, the stochastic process is adapted locally to the respective dynamical flow regime. Our stochastic dual-weighted error estimator is shown to provide meaningful error bounds for a range of physically relevant goals. We prove, as well as show numerically, that our approach can be interpreted as a linearized stochastic-physics ensemble. © 2017 Elsevier Inc.