The features of the of truncation and approximation errors’ geometry on the ensemble of numerical solutions

Alekseev, A. K.; Bondarev, A. E.

doi:10.20948/prepr-2019-107

Cited by 2 publications

(7 citation statements)

References 32 publications

(29 reference statements)

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“…The strict orthogonality of approximation errors is not observed in numerical tests [19]. However, the approximation errors are not collinear also.…”

Section: Distance Between Solutions As the Measure Of The Errormentioning

confidence: 87%

“…For the ensemble of five solutions the results of [18] shows Ieff≈0.6÷4. Tests by [19] demonstrates the efficiency index to be in the range Ieff~0.04÷1.5 (K=2) and Ieff~1.1÷1.5, for K=13.…”

Section: Distances Between Solutionsmentioning

confidence: 99%

“…The above considered error estimators are nonintrusive and are based on a postprocessor. We list and discuss the efficiency index (obtained for numerical solution of the compressible Euler equations [14][15][16][17][18][19], containing shock waves and contact discontinuities), the order of the unresolved error and computational expense for this estimators. This approach uses several consequent grids (minimum two) and, so it is of the medium computational expense.…”

Section: The Comparison Of the Error Estimatorsmentioning

confidence: 99%

“…Another branch of nonstrict a posteriori error estimation methods has a non-intrusive form of certain postprocessor that significantly reduces efforts for coding and debugging. It may be based on the Runge rule [5], Richardson extrapolation (RE) [13,14], Inverse Problem based approach (IP) [15] or ensemble based methods (EM) [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…The computationally cheap approach to a posteriori error estimation that is based on the ensemble of numerical solutions obtained by independent methods is offered by [16][17][18][19]. However, these approaches do not provide the pointwise information on the approximation error.…”

Section: Introductionmentioning

confidence: 99%

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Nonstrict methods for a posteriori error estimation

Bondarev

Alekseev

2020

CPT2020 the 8th International Scientific Conference on Computing in Physics and Technology Proceedings

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The paper is devoted to comparison of a posteriori methods (based on the precomputed solutions) for approximation error estimation. Rigorous a posteriori error estimation for computational Fluid Dynamics at present is practically impossible due to nonlinearity and the discontinuities that may occur and migrate along the flow field. In this situation, several nonstrict (weak) forms of a posteriori estimation of the approximation error may be considered. They either do not provide the error norm estimation in the form of inequalities or provide values of the effectivity index to be less than unit. The best quality of estimates are provided by the Richardson extrapolation, unfortunately for the cost of extremely high computational burden. We pay the special attention to the nonstrict methods that either cannot be presented in a form of inequalities, or demonstrate the effectivity index of an estimator to be below unit. Several new, computationally inexpensive methods for both the point-wise error and the error norm estimation are considered. They are nonintrusive, realized by postprocessing and provide a successful compromise of the reliability and computational efforts. Methods based on the use of an ensemble of independent solutions can be implemented by constructing a generalized computational experiment, which sharply increases the speed and efficiency of the assessment.

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“…The strict orthogonality of approximation errors is not observed in numerical tests [19]. However, the approximation errors are not collinear also.…”

Section: Distance Between Solutions As the Measure Of The Errormentioning

confidence: 87%

Section: Distances Between Solutionsmentioning

confidence: 99%

Section: The Comparison Of the Error Estimatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonstrict methods for a posteriori error estimation

Bondarev

Alekseev

2020

CPT2020 the 8th International Scientific Conference on Computing in Physics and Technology Proceedings

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On the Prager-Synge method for a posteriori error

Alekseev

Bondarev

2021

KIAM Prepr.

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The classic method by Prager and Synge ("hypercircle" method) for a posteriori error estimation in addressed from the viewpoint of the extension of the applicability domain (the range of analyzed problems and methods of the realization). The nonintrusive version of the approximation error estimation that implements the method by Prager and Synge for the arbitrary PDE system is presented. The semiheuristical variant of the Prager and Synge method may be related with the modern approaches for approximation error estimation on the ensemble of solutions obtained by the algorithms of different inner structure.

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The features of the of truncation and approximation errors’ geometry on the ensemble of numerical solutions

Cited by 2 publications

References 32 publications

Nonstrict methods for a posteriori error estimation

Nonstrict methods for a posteriori error estimation

On the Prager-Synge method for a posteriori error

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