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Calcolo
Published in: Calcolo 2/2021

01-06-2021

Superconvergence of the space-time discontinuous Galerkin method for linear nonhomogeneous hyperbolic equations

Authors: Hongling Hu, Chuanmiao Chen, Shufang Hu, Kejia Pan

Published in: Calcolo | Issue 2/2021

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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 \((2n+1)\)-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 \(2n+\frac{1}{2}\) 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.
previous article Pressure-robust error estimate of optimal order for the Stokes equations: domains with re-entrant edges and anisotropic mesh grading
next article Structure-preserving Gauss methods for the nonlinear Schrödinger equation
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Metadata
Title
Superconvergence of the space-time discontinuous Galerkin method for linear nonhomogeneous hyperbolic equations
Authors
Hongling Hu
Chuanmiao Chen
Shufang Hu
Kejia Pan
Publication date
01-06-2021
Publisher
Springer International Publishing
Published in
Calcolo / Issue 2/2021
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-021-00408-7

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