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

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,...

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Bibliographic Details
Published in:Studies in applied mathematics (Cambridge) 2024-11, Vol.153 (4), p.n/a
Main Authors: Georgoulis, Emmanuil H., Hall, Edward J. C., Makridakis, Charalambos G.
Format: Article
Language:English
Subjects:
a posteriori error bounds
discontinuous Galerkin methods
Error analysis
Galerkin method
Polynomials
Runge-Kutta method
Runge–Kutta methods
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Summary: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.
ISSN:0022-2526
1467-9590
DOI:10.1111/sapm.12772