Uniqueness of the best approximation in mean of vector-valued functions

1986 ◽  
Vol 39 (3) ◽  
pp. 183-189
Author(s):  
A. L. Garkavi
Keyword(s):  
Best Approximation ◽  
The Best Approximation ◽  
Vector Valued Functions ◽  
Vector Valued

scholarly journals Finite element quasi-interpolation and best approximation

2017 ◽  
Vol 51 (4) ◽  
pp. 1367-1385 ◽  
Author(s):  
Alexandre Ern ◽  
Jean-Luc Guermond
Keyword(s):  
Finite Element ◽  
Best Approximation ◽  
Approximation Error ◽  
Fractional Sobolev Spaces ◽  
Element Space ◽  
The Best Approximation ◽  
Smoothness Index ◽  
Affine Shape ◽  
Space Point ◽  
Vector Valued

This paper introduces a quasi-interpolation operator for scalar- and vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces. This operator gives optimal estimates of the best approximation error in any Lp-norm assuming regularity in the fractional Sobolev spaces Wr,p, where p ∈ [ 1,∞ ] and the smoothness index r can be arbitrarily close to zero. The operator is stable in L1, leaves the corresponding finite element space point-wise invariant, and can be modified to handle homogeneous boundary conditions. The theory is illustrated on H1-, H(curl)- and H(div)-conforming spaces.

scholarly journals Farkas-Type Results for Vector-Valued Functions with Applications

2017 ◽  
Vol 173 (2) ◽  
pp. 357-390 ◽  
Author(s):  
N. Dinh ◽  
M. A. Goberna ◽  
M. A. López ◽  
T. H. Mo
Keyword(s):  
Vector Valued Functions ◽  
Vector Valued

Intracranial volume-pressure relationship in man

1982 ◽  
Vol 56 (4) ◽  
pp. 524-528 ◽  
Author(s):  
Joseph Th. J. Tans ◽  
Dick C. J. Poortvliet
Keyword(s):  
Best Approximation ◽  
Continuous Monitoring ◽  
Fluid Pressure ◽  
Constant Term ◽  
Volume Index ◽  
Intracranial Volume ◽  
Content Type ◽  
The Best Approximation ◽  
Ventricular Fluid Pressure ◽  
Fine Print

✓ The pressure-volume index (PVI) was determined in 40 patients who underwent continuous monitoring of ventricular fluid pressure. The PVI value was calculated using different mathematical models. From the differences between these values, it is concluded that a monoexponential relationship with a constant term provides the best approximation of the PVI.

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