Convergence and Error Analysis for the  Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows

We construct a numerical scheme based on the scalar auxiliary variable (SAV) approach in time and the MAC discretization in space for the Cahn–Hilliard–Navier–Stokes phase- field model, prove its energy stability, and carry out error analysis for the corresponding Cahn–Hilliard–Stokes model only. The scheme is linear, second-order, unconditionally energy stable and can be implemented very efficiently. We establish second-order error estimates both in time and space for phase-field variable, chemical potential, velocity and pressure in different discrete norms for the Cahn–Hilliard–Stokes phase-field model. We also provide numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy of our scheme.

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Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows

Numerische Mathematik ◽

10.1007/s00211-020-01112-4 ◽

2020 ◽

Vol 145 (1) ◽

pp. 167-196

Author(s):

Hongtao Chen ◽

Jingjing Mao ◽

Jie Shen

Keyword(s):

Finite Element ◽

Error Estimates ◽

Auxiliary Variable ◽

Optimal Error Estimates ◽

Gradient Flows ◽

Optimal Error ◽

Finite Element Schemes

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The stabilized-trigonometric scalar auxiliary variable approach for gradient flows and its efficient schemes

Journal of Engineering Mathematics ◽

10.1007/s10665-021-10155-x ◽

2021 ◽

Vol 129 (1) ◽

Author(s):

Junxiang Yang ◽

Junseok Kim

Keyword(s):

Auxiliary Variable ◽

Gradient Flows ◽

Variable Approach

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The O–C diagrams of minor planets − a new approach to modelling the rotation

International Astronomical Union Colloquium ◽

10.1017/s0252921100031407 ◽

1999 ◽

Vol 173 ◽

pp. 185-188

Author(s):

Gy. Szabó ◽

K. Sárneczky ◽

L.L. Kiss

Keyword(s):

Error Analysis ◽

Time Dependence ◽

Theoretical Work ◽

Minor Planet ◽

Minor Planets ◽

New Approach ◽

Preliminary Results ◽

Ccd Observations

AbstractA widely used tool in studying quasi-monoperiodic processes is the O–C diagram. This paper deals with the application of this diagram in minor planet studies. The main difference between our approach and the classical O–C diagram is that we transform the epoch (=time) dependence into the geocentric longitude domain. We outline a rotation modelling using this modified O–C and illustrate the abilities with detailed error analysis. The primary assumption, that the monotonity and the shape of this diagram is (almost) independent of the geometry of the asteroids is discussed and tested. The monotonity enables an unambiguous distinction between the prograde and retrograde rotation, thus the four-fold (or in some cases the two-fold) ambiguities can be avoided. This turned out to be the main advantage of the O–C examination. As an extension to the theoretical work, we present some preliminary results on 1727 Mette based on new CCD observations.

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Error Analysis in Neuropsychological Assessment of Verbal Memory and Learning

European Journal of Psychological Assessment ◽

10.1027/1015-5759.11.1.21 ◽

1995 ◽

Vol 11 (1) ◽

pp. 21-28 ◽

Cited By ~ 5

Author(s):

Dietmar Heubrock

Keyword(s):

Error Analysis ◽

Verbal Memory ◽

Verbal Learning ◽

Learning Disorders ◽

Memory And Learning ◽

Auditory Verbal Learning Test ◽

Additional Information ◽

Auditory Verbal Learning ◽

Accurate Picture ◽

Learning Test

Performance on a German version of the Rey Auditory-Verbal Learning Test (AVLT) was investigated for 64 juvenile patients who were subdivided in 6 clinical groups. In addition to standard evaluation of AVLT protocols which is usually confined to items recalled correctly, an error analysis was performed. Differentiating between total errors (TE), repetition errors (RE), and misnamings (ME), substantial differences between clinical groups could be demonstrated. It is argued that error analysis of verbal memory and learning enriches the understanding of neuropsychological syndromes, and provides additional information for diagnostic and clinical use. Thus, it is possible to gain a more accurate picture so that patients can be appropriately retrained, and research into the functional causes of memory and learning disorders can be intensified.

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