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Journal of Scientific Computing

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01-04-2021

Computable Interpolation Error Constants for the Geometric Simplex Finite Elements

Authors: Tingting Hao, Xiaofei Guan, Shipeng Mao, Shaochun Chen

Published in: Journal of Scientific Computing | Issue 1/2021

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Abstract

In this paper, a novel high accuracy computation method for interpolation error constants is proposed over the geometric simplex finite elements. Firstly, the expansions of bounded linear operators are employed to derive the explicit estimate of interpolation error constants, which depend only on the shape of the geometric simplex finite elements and the definition of interpolation functions. Then, this method is applied to the linear interpolation function, and the results are consistent with our analysis. Finally, some numerical examples are given to validate our analysis. Such high accuracy computation method for interpolation error constants are beneficial attempts to accelerate the adaptive computation and verification of finite element solutions.

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Title: Computable Interpolation Error Constants for the Geometric Simplex Finite Elements
Authors: Tingting Hao
Xiaofei Guan
Shipeng Mao
Shaochun Chen
Publication date: 01-04-2021
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2021
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-021-01449-4

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