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Stability and Convergence of the Integral-Averaged Interpolation Operator Based on Q1-Element in Rn

Stability and Convergence of the Integral-Averaged Interpolation Operator Based on $Q_1$-Element in $\mathbb{R}^n$

Year:    2024

Author:    Yaru Liu, Yinnian He, Xinlong Feng

Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 2 : pp. 494–513

Abstract

In this paper, we propose an integral-averaged interpolation operator Iτ in a bounded domain Rn by using Q1-element. The interpolation coefficient is defined by the average integral value of the interpolation function u on the interval formed by the midpoints of the neighboring elements. The operator Iτ reduces the regularity requirement for the function u while maintaining standard convergence. Moreover, it possesses an important property of ||Iτu||0,||u||0,. We conduct stability analysis and error estimation for the operator Iτ. Finally, we present several numerical examples to test the efficiency and high accuracy of the operator.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2023-0122

Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 2 : pp. 494–513

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Integral-averaged interpolation operator Q1-element stability convergence.

Author Details

Yaru Liu Email

Yinnian He Email

Xinlong Feng Email

  1. A difference finite element method based on the conforming P1(x,y)×Q1(z,s) element for the 4D Poisson equation

    Liu, Yaru

    He, Yinnian

    Sheen, Dongwoo

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    Computers & Mathematics with Applications, Vol. 174 (2024), Iss. P.18

    https://doi.org/10.1016/j.camwa.2024.08.016 [Citations: 1]