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A posteriori discontinuous Galerkin error estimates for transient convection-diffusion equations. (English) Zbl 1084.65092
The article deals with an analysis of the discontinuous Galerkin method for the convection-diffusion equation. The authors use a nonsymmetric interior penalty formulation, present the local discontinuous Galerkin formulation, derive a posteriori estimates and demonstrate the behaviour of their approach by means of a series of computational examples. Their work is related to this one of B. Rivière and M. F. Wheeler [Comput. Math. Appl. 46, No. 1, 141–163 (2003; Zbl 1059.65098)].

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
65N15 Error bounds for boundary value problems involving PDEs
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