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Goal-oriented a posteriori error estimation for the travel time functional in porous media flows

Cliffe, Andrew; Collis, Joe; Houston, Paul

Authors

Andrew Cliffe Andrew.Cliffe@nottingham.ac.uk

Joe Collis Joe.Collis@nottingham.ac.uk

PAUL HOUSTON paul.houston@nottingham.ac.uk
Professor of Computational and Applied Maths



Abstract

In this article we consider the a posteriori error estimation and adaptive mesh refinement for the numerical approximation of the travel time functional arising in porous media flows. The key application of this work is in the safety assessment of radioactive waste facilities; in this setting, the travel time functional measures the time taken for a non-sorbing radioactive solute, transported by groundwater, to travel from a potential site deep underground to the biosphere. To ensure the computability of the travel time functional, we employ a mixed formulation of Darcy's law and conservation of mass, together with Raviart-Thomas H(div) conforming finite elements. The proposed a posteriori error bound is derived based on a variant of the standard Dual-Weighted-Residual approximation, which takes into account the lack of smoothness of the underlying functional of interest. The proposed adaptive refinement strategy is tested on both a simple academic test case and a problem based on the geological units found at the Sellafield site in the UK.

Journal Article Type Article
Publication Date Jan 1, 2015
Journal SIAM Journal on Scientific Computing
Print ISSN 1064-8275
Electronic ISSN 1064-8275
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 37
Issue 2
Article Number B127-B152
APA6 Citation Cliffe, A., Collis, J., & Houston, P. (2015). Goal-oriented a posteriori error estimation for the travel time functional in porous media flows. SIAM Journal on Scientific Computing, 37(2), doi:10.1137/140960499
DOI https://doi.org/10.1137/140960499
Keywords Travel time functional, groundwater flows, adaptivity, goal-oriented a posteriori error estimation, mixed finite element methods
Publisher URL http://epubs.siam.org/doi/10.1137/140960499
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information Copyright Society for Industrial and Applied Mathematics

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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