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The local discontinuous Galerkin method for advection-diffusion equations arising in groundwater and surface water applications. (English) Zbl 1179.76049
Chadam, John (ed.) et al., Resource recovery, confinement, and remediation of environmental hazards. IMA Workshops: Univ. of Minnesota, Minneapolis, MN, USA, January 15–19, 2000 and February 9–13, 2000. New York, NY: Springer (ISBN 0-387-95506-2). IMA Vol. Math. Appl. 131, 231-245 (2002).
Summary: We describe a discontinuous finite element method for groundwater and surface water applications, based on the Local Discontinuous Galerkin method of B. Cockburn and C. W. Shu [SIAM J. Numer. Anal. 35, No. 6, 2440–2463 (1998; Zbl 0927.65118)]. 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.
For the entire collection see [Zbl 0996.00049].

76M10 Finite element methods applied to problems in fluid mechanics
76R99 Diffusion and convection
86A05 Hydrology, hydrography, oceanography
86-08 Computational methods for problems pertaining to geophysics
35Q35 PDEs in connection with fluid mechanics
35L65 Hyperbolic conservation laws
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs