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

Cliffe, Andrew and Collis, Joe and Houston, Paul (2015) Goal-oriented a posteriori error estimation for the travel time functional in porous media flows. SIAM Journal on Scientific Computing, 37 (2). B127-B152. ISSN 1064-8275

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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.

Item Type: Article
Additional Information: Copyright Society for Industrial and Applied Mathematics
Keywords: Travel time functional, groundwater flows, adaptivity, goal-oriented a posteriori error estimation, mixed finite element methods
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1137/140960499
Depositing User: Houston, Paul
Date Deposited: 26 Aug 2015 10:23
Last Modified: 15 Sep 2016 18:47
URI: http://eprints.nottingham.ac.uk/id/eprint/29672

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