Optimal and Pressure-Independent L² Velocity Error Estimates for a Modified Crouzeix-Raviart Stokes Element with BDM Reconstructions

2015 ◽  
Vol 33 (2) ◽  
pp. 191-208 ◽  
Author(s):  
C. Brennecke
Keyword(s):  
Error Estimates ◽  
Velocity Error ◽  
Pressure Independent

scholarly journals Guaranteed Upper Bounds For The Velocity Error Of Pressure-Robust Stokes Discretisations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
P.L. Lederer ◽  
C. Merdon
Keyword(s):  
Mixed Methods ◽  
Error Control ◽  
Stokes Problem ◽  
Upper Bounds ◽  
Type Result ◽  
Numerical Examples ◽  
Velocity Error ◽  
Divergence Free ◽  
Pressure Independent ◽  
Primal And Dual

Abstract This paper aims to improve guaranteed error control for the Stokes problem with a focus on pressure-robustness, i.e. for discretisations that compute a discrete velocity that is independent of the exact pressure. A Prager-Synge type result relates the velocity errors of divergence-free primal and perfectly equilibrated dual mixed methods for the velocity stress. The first main result of the paper is a framework with relaxed constraints on the primal and dual method. This enables to use a recently developed mass conserving mixed stress discretisation for the design of equilibrated fluxes and to obtain pressure-independent guaranteed upper bounds for any pressure-robust (not necessarily divergence-free) primal discretisation. The second main result is a provably efficient local design of the equilibrated fluxes with comparably low numerical costs. Numerical examples verify the theoretical findings and show that efficiency indices of our novel guaranteed upper bounds are close to one.

Systematic effects in observed parallaxes

1978 ◽  
Vol 48 ◽  
pp. 31-35
Author(s):  
R. B. Hanson
Keyword(s):  
Error Estimates ◽  
Zero Point ◽  
Absolute Zero ◽  
Apparent Magnitude ◽  
Coherent System ◽  
Preliminary Results ◽  
General Catalogue ◽  
Systematic Effects ◽  
New Evidence ◽  
Right Ascension

Several outstanding problems affecting the existing parallaxes should be resolved to form a coherent system for the new General Catalogue proposed by van Altena, as well as to improve luminosity calibrations and other parallax applications. Lutz has reviewed several of these problems, such as: (A) systematic differences between observatories, (B) external error estimates, (C) the absolute zero point, and (D) systematic observational effects (in right ascension, declination, apparent magnitude, etc.). Here we explore the use of cluster and spectroscopic parallaxes, and the distributions of observed parallaxes, to bring new evidence to bear on these classic problems. Several preliminary results have been obtained.

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