Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Error estimation and uncertainty quantification for first time to a
  threshold value   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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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th