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A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems. (English) Zbl 0998.65098
The paper presents a spatial discretisation error analysis for discontinuous Galerkin methods in the context of one-dimensional hyperbolic conservation laws. The results are used to construct asymptotically correct a posteriori estimates of spatial discretisation errors that are effective for linear and nonlinear conservation laws in regions where the solution is smooth.

MSC:
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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