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

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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