scholarly journals Approximation by quasi-interpolation operators and Smolyak's algorithm

2021 ◽  
pp. 101601
Author(s):  
Yurii Kolomoitsev
Keyword(s):  
Interpolation Operators ◽  
Smolyak's Algorithm

scholarly journals $$H^1$$-conforming finite element cochain complexes and commuting quasi-interpolation operators on Cartesian meshes

CALCOLO ◽  
2021 ◽  
Vol 58 (2) ◽  
Author(s):  
Francesca Bonizzoni ◽  
Guido Kanschat
Keyword(s):  
Finite Element ◽  
Tensor Product ◽  
Arbitrary Order ◽  
Inner Product ◽  
Cochain Complex ◽  
Exterior Derivative ◽  
Product Construction ◽  
Cartesian Meshes ◽  
Conforming Finite Element ◽  
Interpolation Operators

AbstractA finite element cochain complex on Cartesian meshes of any dimension based on the $$H^1$$ H 1 -inner product is introduced. It yields $$H^1$$ H 1 -conforming finite element spaces with exterior derivatives in $$H^1$$ H 1 . We use a tensor product construction to obtain $$L^2$$ L 2 -stable projectors into these spaces which commute with the exterior derivative. The finite element complex is generalized to a family of arbitrary order.

scholarly journals Applications of Interpolation Operators

2015 ◽  
Vol 20 (2) ◽  
pp. 1-4
Author(s):  
Alina Baboş
Keyword(s):  
Interpolation Operators

Abstract We use Lagrange, Hermite and Birkhoff operator that interpolates a function f and certain of its derivatives, defined on a triangle, for construction of some surfaces. We construct this type of surfaces using concrete examples.

Approximation based on elliptic splines

2014 ◽  
Vol 12 (05) ◽  
pp. 1461014 ◽  
Author(s):  
Zhuyuan Yang ◽  
Zongwen Yang
Keyword(s):  
Sobolev Spaces ◽  
Besov Spaces ◽  
Fourier Transforms ◽  
Projection Operators ◽  
Order Of Approximation ◽  
B Splines ◽  
Interpolation Operators ◽  
Polynomial Reproducing

In this paper, we study the elliptic splines which include the well-known polyharmonic B-splines. We analyze their Fourier transforms, decay behaviors and polynomial reproducing properties. We also study the order of approximation in Sobolev spaces and consider their characterizations of Besov spaces by the scale projection operators, quasi-interpolation operators and wavelet operators.

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