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Control Parametrization and Finite Element Method for Controlling Multi-species Reactive Transport in an Underground Channel

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Abstract

In this paper, a cleaning program involving effluent discharge of several species in a one-dimensional underground channel is considered. Due to environmental health requirements, the outlet concentration of each species at any time during the entire cleaning activities has to be kept at a certain low level in order to offset the deteriorating effect of contaminant destruction. Thus, a computational scheme using combined control parametrization and finite element method is used to develop a cleaning program to meet the above environmental health requirements. Numerical examples have been used to illustrate the efficiency of our method.

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Authors and Affiliations

  1. School of Computational and Applied Mathematics, University of the Witwatersrands, Johannesburg, South Africa

    K. H. Wong & C. Myburgh

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China

    H. W. J. Lee & C. K. Chan

Authors
  1. K. H. Wong
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  2. H. W. J. Lee
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  3. C. K. Chan
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  4. C. Myburgh
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Correspondence to K. H. Wong.

Additional information

Communicated by Kok Lay Teo.

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Wong, K.H., Lee, H.W.J., Chan, C.K. et al. Control Parametrization and Finite Element Method for Controlling Multi-species Reactive Transport in an Underground Channel. J Optim Theory Appl 157, 168–187 (2013). https://doi.org/10.1007/s10957-012-0148-9

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  • DOI: https://doi.org/10.1007/s10957-012-0148-9

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