Quasi-a priori truncation error estimation in the DGSEM

Rubio Calzado, Gonzalo and Fraysse, Francois and Kopriva, David A. and Valero Sánchez, Eusebio (2014). Quasi-a priori truncation error estimation in the DGSEM. "Journal of Scientific Computing", v. 64 (n. 2); pp. 425-455. ISSN 0885-7474. https://doi.org/10.1007/s10915-014-9938-6.


Title: Quasi-a priori truncation error estimation in the DGSEM
  • Rubio Calzado, Gonzalo
  • Fraysse, Francois
  • Kopriva, David A.
  • Valero Sánchez, Eusebio
Item Type: Article
Título de Revista/Publicación: Journal of Scientific Computing
Date: 31 October 2014
ISSN: 0885-7474
Volume: 64
Faculty: E.T.S. de Ingeniería Aeronáutica y del Espacio (UPM)
Department: Matemática Aplicada a la Ingeniería Aeroespacial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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In this paper we show how to accurately perform a quasi-a priori estimation of the truncation error of steady-state solutions computed by a discontinuous Galerkin spectral element method. We estimate the spatial truncation error using the ?-estimation procedure. While most works in the literature rely on fully time-converged solutions on grids with different spacing to perform the estimation, we use non time-converged solutions on one grid with different polynomial orders. The quasi-a priori approach estimates the error while the residual of the time-iterative method is not negligible. Furthermore, the method permits one to decouple the surface and the volume contributions of the truncation error, and provides information about the anisotropy of the solution as well as its rate of convergence in polynomial order. First, we focus on the analysis of one dimensional scalar conservation laws to examine the accuracy of the estimate. Then, we extend the analysis to two dimensional problems. We demonstrate that this quasi-a priori approach yields a spectrally accurate estimate of the truncation error.

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More information

Item ID: 40264
DC Identifier: https://oa.upm.es/40264/
OAI Identifier: oai:oa.upm.es:40264
DOI: 10.1007/s10915-014-9938-6
Official URL: http://link.springer.com/article/10.1007/s10915-014-9938-6
Deposited by: Memoria Investigacion
Deposited on: 03 Oct 2016 11:18
Last Modified: 12 Jun 2019 11:39
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