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We develop an Eulerian‐Lagrangian discontinuous Galerkin method for time‐dependent advection‐diffusion equations. The derived scheme has combined advantages of Eulerian‐Lagrangian methods and discontinuous Galerkin methods. The scheme does not contain any undetermined problem‐dependent parameter. An optimal‐order error estimate and superconvergence estimate is derived. Numerical experiments are presented, which verify the theoretical estimates.
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Wang et al. (2007) studied this question.
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