Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

Wildey, T.

doi:10.1016/J.JCP.2014.09.014

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

Journal Article · Thu Jan 01 04:00:00 EST 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2014.09.014· OSTI ID:22382155

Wildey, T.

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.

OSTI ID:: 22382155

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 280; ISSN JCTPAH; ISSN 0021-9991

Country of Publication:: United States

Language:: English

References (4)

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