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Keywords:

  • characteristic methods;
  • discontinuous Galerkin method;
  • Eulerian-Lagrangian methods;
  • interior penalty methods;
  • uniform error estimates

Abstract

We prove an optimal-order error estimate in a weighted energy norm for the Eulerian-Lagrangian discontinuous Galerkin method for unsteady-state advection–diffusion equations with general inflow and outflow boundary conditions. It is well-known that these problems admit dynamic fronts with interior and boundary layers. The estimate holds uniformly with respect to the vanishing diffusion coefficient. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009