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Quasi-A Priori Truncation Error Estimation in the DGSEM

Gonzalo Rubio, François Fraysse, David A. Kopriva, Eusebio Valero
2014 Journal of Scientific Computing  
We demonstrate that this quasi-a priori approach yields a spectrally accurate estimate of the truncation error.  ...  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.  ...  Acknowledgments This research is supported by the European Project ANADE (PINT-GA-2011-289428).  ... 
doi:10.1007/s10915-014-9938-6 fatcat:q62ugstv4bcdjo4bgktct7tm5u

Adaptation strategies for high order discontinuous Galerkin methods based on Tau-estimation

Moritz Kompenhans, Gonzalo Rubio, Esteban Ferrer, Eusebio Valero
2016 Journal of Computational Physics  
The truncation error is approximated by means of a r-estimation procedure and enables the identification of mesh regions that require adaptation.  ...  In addition, the high order method permits the spatial decoupling for the estimated errors and enables anisotropic p-adaptation.  ...  Proof of the quasi-a priori x -estimation formula, Eq. (31) Substituting the definitions of the iteration error, u r.P estimate of the truncation error Eq. (31) and, using Taylor series, we obtain  ... 
doi:10.1016/j.jcp.2015.11.032 fatcat:rbqzflvgfjbozcrsnblamgrri4

Truncation Error Estimation in the p-Anisotropic Discontinuous Galerkin Spectral Element Method

Andrés M. Rueda-Ramírez, Gonzalo Rubio, Esteban Ferrer, Eusebio Valero
2018 Journal of Scientific Computing  
In this paper, we present a novel anisotropic truncation error estimator derived from the τ-estimation procedure for DGSEM.  ...  This method estimates the truncation error of representations with different polynomial orders using the solution on a reference mesh of relatively high order.  ...  The authors acknowledge the computer resources and technical assistance provided by the Centro de Supercomputación y Visualización de Madrid (CeSViMa).  ... 
doi:10.1007/s10915-018-0772-0 fatcat:uhbgqd3y4zdzpgzcvpwcfc3v3m

On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics [article]

Hendrik Ranocha and Andrew R. Winters and Hugo Guillermo Castro and Lisandro Dalcin and Michael Schlottke-Lakemper and Gregor J. Gassner and Matteo Parsani
2022 arXiv   pre-print
We demonstrate that error-based approaches are convenient in a wide range of applications and compare them to more classical step size control based on a Courant-Friedrichs-Lewy (CFL) number.  ...  such as the Euler equations.  ...  Gregor Gassner acknowledges funding through the Klaus-Tschira Stiftung via the project "HiFiLab".  ... 
arXiv:2209.07037v1 fatcat:hg3honbmkjca7gmrlif6bgm4yi

A p-Multigrid Strategy with Anisotropic p-Adaptation Based on Truncation Errors for High-Order Discontinuous Galerkin Methods [article]

Andrés M. Rueda-Ramírez, Juan Manzanero, Esteban Ferrer, Gonzalo Rubio, Eusebio Valero
2018 pre-print
To achieve this, we show that a recently developed anisotropic truncation error estimator [Rueda-Ramírez et al., Truncation Error Estimation in the p-Anisotropic DGSEM, J. of Scientific Computing] is perfectly  ...  On the one hand, local mesh adaptation strategies based on error estimation have been proposed to reduce the number of degrees of freedom while keeping a similar accuracy.  ...  The authors acknowledge the computer resources and technical assistance provided by the Centro de Supercomputación y Visualización de Madrid (CeSViMa).  ... 
doi:10.1016/j.jcp.2018.11.009 arXiv:1806.11456v1 fatcat:z3lnvh3nszhixa2hyogy6xwruy