A parameter-free smoothness indicator for high-resolution finite element schemes

Dmitri Kuzmin; Friedhelm Schieweck

Open Mathematics (2013)

  • Volume: 11, Issue: 8, page 1478-1488
  • ISSN: 2391-5455

Abstract

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This paper presents a postprocessing technique for estimating the local regularity of numerical solutions in high-resolution finite element schemes. A derivative of degree p ≥ 0 is considered to be smooth if a discontinuous linear reconstruction does not create new maxima or minima. The intended use of this criterion is the identification of smooth cells in the context of p-adaptation or selective flux limiting. As a model problem, we consider a 2D convection equation discretized with bilinear finite elements. The discrete maximum principle is enforced using a linearized flux-corrected transport algorithm. The deactivation of the flux limiter in regions of high regularity makes it possible to avoid the peak clipping effect at smooth extrema without generating spurious undershoots or overshoots elsewhere.

How to cite

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Dmitri Kuzmin, and Friedhelm Schieweck. "A parameter-free smoothness indicator for high-resolution finite element schemes." Open Mathematics 11.8 (2013): 1478-1488. <http://eudml.org/doc/269085>.

@article{DmitriKuzmin2013,
abstract = {This paper presents a postprocessing technique for estimating the local regularity of numerical solutions in high-resolution finite element schemes. A derivative of degree p ≥ 0 is considered to be smooth if a discontinuous linear reconstruction does not create new maxima or minima. The intended use of this criterion is the identification of smooth cells in the context of p-adaptation or selective flux limiting. As a model problem, we consider a 2D convection equation discretized with bilinear finite elements. The discrete maximum principle is enforced using a linearized flux-corrected transport algorithm. The deactivation of the flux limiter in regions of high regularity makes it possible to avoid the peak clipping effect at smooth extrema without generating spurious undershoots or overshoots elsewhere.},
author = {Dmitri Kuzmin, Friedhelm Schieweck},
journal = {Open Mathematics},
keywords = {Finite elements; Maximum principles; Smoothness indicators; Gradient recovery; Slope limiting; Flux-corrected transport; p-adaptation; finite elements; maximum principles; smoothness indicators; gradient recovery; slope limiting; flux-corrected transport; -adaptation; numerical examples; convection equation; algorithm},
language = {eng},
number = {8},
pages = {1478-1488},
title = {A parameter-free smoothness indicator for high-resolution finite element schemes},
url = {http://eudml.org/doc/269085},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Dmitri Kuzmin
AU - Friedhelm Schieweck
TI - A parameter-free smoothness indicator for high-resolution finite element schemes
JO - Open Mathematics
PY - 2013
VL - 11
IS - 8
SP - 1478
EP - 1488
AB - This paper presents a postprocessing technique for estimating the local regularity of numerical solutions in high-resolution finite element schemes. A derivative of degree p ≥ 0 is considered to be smooth if a discontinuous linear reconstruction does not create new maxima or minima. The intended use of this criterion is the identification of smooth cells in the context of p-adaptation or selective flux limiting. As a model problem, we consider a 2D convection equation discretized with bilinear finite elements. The discrete maximum principle is enforced using a linearized flux-corrected transport algorithm. The deactivation of the flux limiter in regions of high regularity makes it possible to avoid the peak clipping effect at smooth extrema without generating spurious undershoots or overshoots elsewhere.
LA - eng
KW - Finite elements; Maximum principles; Smoothness indicators; Gradient recovery; Slope limiting; Flux-corrected transport; p-adaptation; finite elements; maximum principles; smoothness indicators; gradient recovery; slope limiting; flux-corrected transport; -adaptation; numerical examples; convection equation; algorithm
UR - http://eudml.org/doc/269085
ER -

References

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