Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions

Mark Ainsworth; Alejandro Allendes; Gabriel R. Barrenechea; Richard Rankin

doi:10.1002/fld.3822

Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions

Mark Ainsworth, Alejandro Allendes, Gabriel R. Barrenechea, Richard Rankin

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

27 Citations (Scopus)

Abstract

Fully computable upper bounds are developed for the discretisation error measured in the natural (energy) norm for convection-reaction-diffusion problems in three dimensions. The upper bounds are genuine upper bounds in the sense that the numerical value of the estimated error exceeds the actual numerical value of the true error regardless of the coarseness of the mesh or the nature of the data for the problem. All constants appearing in the bounds are fully specified. Examples show the estimator to be reliable and accurate even in the case of complicated three-dimensional problems.

Original language	English
Pages (from-to)	765-790
Number of pages	26
Journal	International Journal of Numerical Methods in Fluids
Volume	73
Issue number	9
DOIs	https://doi.org/10.1002/fld.3822
Publication status	Published - 30 Nov 2013

Keywords

3D convection-reaction-diffusion
SUPG stabilised method
fully computable a posteriori estimator

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10.1002/fld.3822

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abstract = "Fully computable upper bounds are developed for the discretisation error measured in the natural (energy) norm for convection-reaction-diffusion problems in three dimensions. The upper bounds are genuine upper bounds in the sense that the numerical value of the estimated error exceeds the actual numerical value of the true error regardless of the coarseness of the mesh or the nature of the data for the problem. All constants appearing in the bounds are fully specified. Examples show the estimator to be reliable and accurate even in the case of complicated three-dimensional problems.",

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Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions. / Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R. et al.
In: International Journal of Numerical Methods in Fluids, Vol. 73, No. 9, 30.11.2013, p. 765-790.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions

AU - Ainsworth, Mark

AU - Allendes, Alejandro

AU - Barrenechea, Gabriel R.

AU - Rankin, Richard

PY - 2013/11/30

Y1 - 2013/11/30

N2 - Fully computable upper bounds are developed for the discretisation error measured in the natural (energy) norm for convection-reaction-diffusion problems in three dimensions. The upper bounds are genuine upper bounds in the sense that the numerical value of the estimated error exceeds the actual numerical value of the true error regardless of the coarseness of the mesh or the nature of the data for the problem. All constants appearing in the bounds are fully specified. Examples show the estimator to be reliable and accurate even in the case of complicated three-dimensional problems.

AB - Fully computable upper bounds are developed for the discretisation error measured in the natural (energy) norm for convection-reaction-diffusion problems in three dimensions. The upper bounds are genuine upper bounds in the sense that the numerical value of the estimated error exceeds the actual numerical value of the true error regardless of the coarseness of the mesh or the nature of the data for the problem. All constants appearing in the bounds are fully specified. Examples show the estimator to be reliable and accurate even in the case of complicated three-dimensional problems.

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KW - SUPG stabilised method

KW - fully computable a posteriori estimator

U2 - 10.1002/fld.3822

DO - 10.1002/fld.3822

M3 - Article

SN - 0271-2091

VL - 73

SP - 765

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JO - International Journal of Numerical Methods in Fluids

JF - International Journal of Numerical Methods in Fluids

IS - 9

ER -

Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions

Abstract

Keywords

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