Displaying similar documents to “Interpolation with restrictions -- role of the boundary conditions and individual restrictions”

Three ways of interpolation on finite elements

Šolín, Pavel, Segeth, Karel

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Interpolation on finite elements usually occurs in a Hilbert space setting, which means that interpolation techniques involving orthogonal projection are an alternative for the traditional Lagrange nodal interpolation schemes. In addition to the Lagrange interpolation, this paper discusses the global orthogonal projection and the projection-based interpolation. These techniques are compared from the point of view of quality, efficiency, sensitivity to input parameters and other aspects....

Extending Babuška-Aziz's theorem to higher-order Lagrange interpolation

Kenta Kobayashi, Takuya Tsuchiya (2016)

Applications of Mathematics

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We consider the error analysis of Lagrange interpolation on triangles and tetrahedrons. For Lagrange interpolation of order one, Babuška and Aziz showed that squeezing a right isosceles triangle perpendicularly does not deteriorate the optimal approximation order. We extend their technique and result to higher-order Lagrange interpolation on both triangles and tetrahedrons. To this end, we make use of difference quotients of functions with two or three variables. Then, the error estimates...

An extended Prony’s interpolation scheme on an equispaced grid

Dovile Karalienė, Zenonas Navickas, Raimondas Čiegis, Minvydas Ragulskis (2015)

Open Mathematics

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An interpolation scheme on an equispaced grid based on the concept of the minimal order of the linear recurrent sequence is proposed in this paper. This interpolation scheme is exact when the number of nodes corresponds to the order of the linear recurrent function. It is shown that it is still possible to construct a nearest mimicking algebraic interpolant if the order of the linear recurrent function does not exist. The proposed interpolation technique can be considered as the extension...