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On a posteriori error estimation for Runge–Kutta discontinuous Galerkin methods for linear hyperbolic problems

Year: 2024
Type: article
Abstract: A posteriori bounds for the error measured in various norms for a standard second‐order explicit‐in‐time Runge–Kutta discontinuous Galerkin (RKDG) discretization of a one‐dimensional (in space) linear transport problem are derived. The proof is based on a novel space‐time polynomial reconstruction, hinging on high‐order temporal reconstructions for continuous and discontinuous Galerkin time‐stepping methods. Of particular interest is the question of error estimation under dynamic mesh modification. The theoretical findings are tested by numerical experiments.
DOI: 10.1111/sapm.12772
Institutions: National Technical University of Athens, Heriot-Watt University, Maxwell Institute for Mathematical Sciences, FORTH Institute of Applied and Computational Mathematics, Foundation for Research and Technology Hellas, University of Nottingham, University of Crete, University of Sussex
Language: English
Open Access status: hybrid
Estimated APC paid: $4,330
OpenAlex ID: W4403338888
FWCI:
Cites: 19
Cited by:
Related to: 10