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

• Autorzy: Dmitri Kuzmin , Friedhelm Schieweck
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Finite elements; Maximum principles; Smoothness indicators; Gradient recovery; Slope limiting; Flux-corrected transport; p-adaptation

Kategorie tematyczne

• 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 8
• Strony: 1478-1488

Daty

wydano

2013-08-01

online

2013-05-22

Twórcy

autor

Dmitri Kuzmin

• Friedrich-Alexander-Universität Erlangen-Nürnberg

autor

Friedhelm Schieweck

• Otto-von-Guericke-Universität Magdeburg

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0254-4