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 $I_\tau$ in a bounded domain $Ω ⊂ \mathbb{R}^n$ by using $Q_1$-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 $I_\tau$ reduces the regularity requirement for the function $u$ while maintaining standard convergence. Moreover, it possesses an important property of $||I_\tau u||_{0,Ω} ≤ ||u||_{0,Ω}.$ We conduct stability analysis and error estimation for the operator $I\tau.$ 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 $Q_1$-element stability convergence.
Author Details
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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
Feng, Xinlong
Computers & Mathematics with Applications, Vol. 174 (2024), Iss. P.18
https://doi.org/10.1016/j.camwa.2024.08.016 [Citations: 1]