Displaying similar documents to “Interpolation Error Estimates for the Reduced Hsieh-Clough-Tocher Triangle”

A priori error estimates for Lagrange interpolation on triangles

Kenta Kobayashi, Takuya Tsuchiya (2015)

Applications of Mathematics

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We present the error analysis of Lagrange interpolation on triangles. A new a priori error estimate is derived in which the bound is expressed in terms of the diameter and circumradius of a triangle. No geometric conditions on triangles are imposed in order to get this type of error estimates. To derive the new error estimate, we make use of the two key observations. The first is that squeezing a right isosceles triangle perpendicularly does not reduce the approximation property of Lagrange...

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.