Abstract
We present a study of the local discontinuous Galerkin method for transient convection–diffusion problems in one dimension. We show that p-degree piecewise polynomial discontinuous finite element solutions of convection-dominated problems are O(Δx p+2) superconvergent at Radau points. For diffusion- dominated problems, the solution’s derivative is O(Δx p+2) superconvergent at the roots of the derivative of Radau polynomial of degree p+1. Using these results, we construct several asymptotically exact a posteriori finite element error estimates. Computational results reveal that the error estimates are asymptotically exact.
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Adjerid, S., Klauser, A. Superconvergence of Discontinuous Finite Element Solutions for Transient Convection–diffusion Problems. J Sci Comput 22, 5–24 (2005). https://doi.org/10.1007/s10915-004-4133-9
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DOI: https://doi.org/10.1007/s10915-004-4133-9