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The Local Discontinuous Galerkin Method for Advection-Diffusion Equations Arising in Groundwater and Surface Water Applications

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Resource Recovery, Confinement, and Remediation of Environmental Hazards

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 131))

Abstract

We describe a discontinuous finite element method for groundwater and surface water applications, based on the local discontinuous Galerkin method of Cockburn and Shu [16] . This method is defined locally over each element, allows for the use of different approximating polynomials in different elements, and allows for nonconforming elements. Upwinding is built into the method for stability in advection-dominated cases. The method is also locally and globally conservative. We describe the method for fairly general multi-dimensional systems of nonlinear advection-diffusion equations, and then give some numerical results specifically for contaminant transport in groundwater and surface water hydrodynamics.

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Author information

Authors and Affiliations

  1. Center for Subsurface Modeling, Texas Institute for Computational and Applied Mathematics, University of Texas at Austin, Austin, TX, 78712, USA

    Clint Dawson & Vadym Aizinger

Authors
  1. Clint Dawson
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  2. Vadym Aizinger
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    John Chadam

  2. Center for Biofilm Engineering, Montana State University, Bozeman, MT, 59717-3980, USA

    Al Cunningham (CBE Industry/Education Initiatives Coordinator) (CBE Industry/Education Initiatives Coordinator)

  3. Institute for Scientific Computation, Department of Mathematics, Texas A&M University, College Station, TX, 77843-3404, USA

    Richard E. Ewing

  4. Laboratory for Computational Geodynamics, Chemistry Building, Indiana University, Bloomington, IN, 47405, USA

    Peter Ortoleva

  5. Texas Institute for Computational and Applied Mathematics (TICAM), The University of Texas at Austin, Austin, TX, 78712, USA

    Mary Fanett Wheeler

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Dawson, C., Aizinger, V. (2002). The Local Discontinuous Galerkin Method for Advection-Diffusion Equations Arising in Groundwater and Surface Water Applications. In: Chadam, J., Cunningham, A., Ewing, R.E., Ortoleva, P., Wheeler, M.F. (eds) Resource Recovery, Confinement, and Remediation of Environmental Hazards. The IMA Volumes in Mathematics and its Applications, vol 131. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0037-3_13

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  • DOI: https://doi.org/10.1007/978-1-4613-0037-3_13

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6553-5

  • Online ISBN: 978-1-4613-0037-3

  • eBook Packages: Springer Book Archive

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