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$hp$-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes

Published 20 Oct 2023 in math.NA and cs.NA | (2310.13564v4)

Abstract: We prove hp-optimal error estimates for the original DG method when approximating solutions to first-order hyperbolic problems with constant convection fields in the L2 and DG norms. The main theoretical tools used in the analysis are novel hp-optimal approximation properties of the special projector introduced in [Cockburn, Dong, Guzman, SINUM, 2008]. We assess the theoretical findings on some test cases.

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Authors (2)

  1. Zhaonan Dong 
  2. Lorenzo Mascotto 

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