Displaying similar documents to “Asymptotic formulas for the error in linear interpolation”

On the interpolation constants over triangular elements

Kobayashi, Kenta

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We propose a simple method to obtain sharp upper bounds for the interpolation error constants over the given triangular elements. These constants are important for analysis of interpolation error and especially for the error analysis in the Finite Element Method. In our method, interpolation constants are bounded by the product of the solution of corresponding finite dimensional eigenvalue problems and constant which is slightly larger than one. Guaranteed upper bounds for these constants...

Anisotropic interpolation error estimates via orthogonal expansions

Mingxia Li, Shipeng Mao (2013)

Open Mathematics

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We prove anisotropic interpolation error estimates for quadrilateral and hexahedral elements with all possible shape function spaces, which cover the intermediate families, tensor product families and serendipity families. Moreover, we show that the anisotropic interpolation error estimates hold for derivatives of any order. This goal is accomplished by investigating an interpolation defined via orthogonal expansions.

Error estimates for some quasi-interpolation operators

Rüdiger Verfürth (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We derive explicit bounds on the constants in error estimates for two quasi-interpolation operators which are modifications of the “classical” Clément-operator. These estimates are crucial for making explicit the constants which appear in popular error estimates. They are also compared with corresponding estimates for the standard nodal interpolation operator.

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...