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

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Kuzmin D., Schieweck F.

Open Mathematics

2013

tom 11

nr 8

1478-1488

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.

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1 Open Mathematics

1 Kuzmin D.

1 Schieweck F.

1 2013

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