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- Title
Superconvergence of the space-time discontinuous Galerkin method for linear nonhomogeneous hyperbolic equations.
- Authors
Hu, Hongling; Chen, Chuanmiao; Hu, Shufang; Pan, Kejia
- Abstract
In this study, we discuss the superconvergence of the space-time discontinuous Galerkin method for the first-order linear nonhomogeneous hyperbolic equation. By using the local differential projection method to construct comparison function, we prove that the numerical solution is (2 n + 1) -th order superconvergent at the downwind-biased Radau points in the discrete L 2 -norm. As a by-product, we obtain a point-wise superconvergence with order 2 n + 1 2 in vertices. We also find that, in order to obtain these superconvergence results, the source integral term has to be approximated by (n + 1) -point Radau-quadrature rule. Numerical results are presented to verify our theoretical findings.
- Subjects
GALERKIN methods; SPACETIME; EQUATIONS; HYPERBOLIC differential equations; QUADRATURE domains
- Publication
Calcolo, 2021, Vol 58, Issue 2, p1
- ISSN
0008-0624
- Publication type
Article
- DOI
10.1007/s10092-021-00408-7