Stochastic variational multiscale method for error estimation and adaptivity in uncertain transport problems

Li, Jason
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Sahni, Onkar
Li, Fengyan
Oberai, Assad
Shephard, M. S. (Mark S.)
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Aeronautical engineering
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Similarly, a model term is derived to explicitly estimate the error in a local or element-wise fashion. This model term is approximated using the components of the stabilization parameter used in computing the numerical solution, making error estimation computationally inexpensive. We compare the error estimator with either the true error or a reference error from a much finer discretization, with which our error estimator agrees very well both locally and globally. Further, procedures using the local error estimator are designed to drive adaptivity in the physical domain and in the stochastic domain. In the physical domain, we apply mesh adaptation. Likewise, stochastic adaptivity controls the local spectral approximation (i.e., a spatially varying spectral order over the mesh). We propose two schemes for adaptivity and apply them to mesh adaptivity and stochastic adaptivity individually. We demonstrate adaptivity on several transport problems with up to three orders of savings in the number of degrees-of-freedom for a given level of accuracy.
May 2018
School of Engineering
Dept. of Mechanical, Aerospace, and Nuclear Engineering
Rensselaer Polytechnic Institute, Troy, NY
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