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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
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
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
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
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