Goal-oriented a posteriori error estimation for the travel time functional in porous media flows
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...
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| Format: | Article |
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Society for Industrial and Applied Mathematics
2015
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| Online Access: | https://eprints.nottingham.ac.uk/29672/ |
| _version_ | 1848793827856351232 |
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| author | Cliffe, Andrew Collis, Joe Houston, Paul |
| author_facet | Cliffe, Andrew Collis, Joe Houston, Paul |
| author_sort | Cliffe, Andrew |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:06:29Z |
| format | Article |
| id | nottingham-29672 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:06:29Z |
| publishDate | 2015 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-296722020-05-04T20:10:44Z https://eprints.nottingham.ac.uk/29672/ Goal-oriented a posteriori error estimation for the travel time functional in porous media flows Cliffe, Andrew Collis, Joe Houston, Paul 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. Society for Industrial and Applied Mathematics 2015 Article PeerReviewed Cliffe, Andrew, 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 Travel time functional groundwater flows adaptivity goal-oriented a posteriori error estimation mixed finite element methods http://epubs.siam.org/doi/10.1137/140960499 doi:10.1137/140960499 doi:10.1137/140960499 |
| spellingShingle | Travel time functional groundwater flows adaptivity goal-oriented a posteriori error estimation mixed finite element methods Cliffe, Andrew Collis, Joe Houston, Paul Goal-oriented a posteriori error estimation for the travel time functional in porous media flows |
| title | Goal-oriented a posteriori error estimation for the travel time functional in porous media flows |
| title_full | Goal-oriented a posteriori error estimation for the travel time functional in porous media flows |
| title_fullStr | Goal-oriented a posteriori error estimation for the travel time functional in porous media flows |
| title_full_unstemmed | Goal-oriented a posteriori error estimation for the travel time functional in porous media flows |
| title_short | Goal-oriented a posteriori error estimation for the travel time functional in porous media flows |
| title_sort | goal-oriented a posteriori error estimation for the travel time functional in porous media flows |
| topic | Travel time functional groundwater flows adaptivity goal-oriented a posteriori error estimation mixed finite element methods |
| url | https://eprints.nottingham.ac.uk/29672/ https://eprints.nottingham.ac.uk/29672/ https://eprints.nottingham.ac.uk/29672/ |