Nitsche’s method as a variational multiscale formulation and a resulting boundary layer fine-scale model

Stoter, Stein K. F.; Eikelder, M.F.P. ten; Prenter, Frits de; Akkerman, I.; Brummelen, E. Harald van; Verhoosel, Clemens V.; Schillinger, Dominik

doi:10.1016/j.cma.2021.113878

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Projection Operators1

The Gibbs Phenomenon In One Dimension1

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2022

2024

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Cited by 4 publications

(2 citation statements)

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“…Additionally, the mapping P IP is idempotent, and is a linear and bounded operator on the space Ṽ × Q × Q. As a consequence, P IP is a projector, and we refer to it as the interior penalty projector [40,41]. The penalty parameter η penalizes mismatches of interface jumps.…”

Section: Projection Operatorsmentioning

confidence: 99%

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Constraints for eliminating the Gibbs phenomenon in finite element approximation spaces

Eikelder¹,

Stoter²,

Bazilevs³

et al. 2023

Preprint

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One of the major challenges in finite element methods is the mitigation of spurious oscillations near sharp layers and discontinuities known as the Gibbs phenomenon. In this article, we propose a set of functionals to identify spurious oscillations in best approximation problems in finite element spaces. Subsequently, we adopt these functionals in the formulation of constraints in an effort to eliminate the Gibbs phenomenon. By enforcing these constraints in best approximation problems, we can entirely eliminate over-and undershoot in one dimensional continuous approximations, and significantly suppress them in one-and higher-dimensional discontinuous approximations.

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Section: Projection Operatorsmentioning

confidence: 99%

“…Furthermore, we observe that the average of the approximation φ h at the element boundaries coincides with the value of φ. This is a property of the interior penalty projector [40].…”

Section: The Gibbs Phenomenon In One Dimensionmentioning

confidence: 99%