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arXiv · 2001.11139

Error estimation and uncertainty quantification for first time to a threshold value

Jehanzeb H. Chaudhry·Donald Estep·Zachary Stevens·Simon J. Tavener
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Abstract

Classical a posteriori error analysis for differential equations quantifies the error in a Quantity of Interest (QoI) which is represented as a bounded linear functional of the solution. In this work we consider a posteriori error estimates of a quantity of interest that cannot be represented in this fashion, namely the time at which a threshold is crossed for the first time. We derive two representations for such errors and use an adjoint-based a posteriori approach to estimate unknown terms that appear in our representation. The first representation is based on linearizations using Taylor's Theorem. The second representation is obtained by implementing standard root-finding techniques. We provide several examples which demonstrate the accuracy of the methods. We then embed these error estimates within a framework to provide error bounds on a cumulative distribution function when parameters of the differential equations are uncertain.

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Jehanzeb H. Chaudhry, Donald Estep, Zachary Stevens, Simon J. Tavener. 2020-01-30. Error estimation and uncertainty quantification for first time to a threshold value. https://arxiv.org/abs/2001.11139

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