@Article{NMTMA-17-2,
author = {Yaru, Liu and Yinnian, He and Xinlong, Feng},
title = {Stability and Convergence of the Integral-Averaged Interpolation Operator Based on $Q_1$-Element in $\mathbb{R}^n$},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2024},
volume = {17},
number = {2},
pages = {494--513},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2023-0122},
url = {https://global-sci.com/article/91268/stability-and-convergence-of-the-integral-averaged-interpolation-operator-based-on-q-1-element-in-mathbbrn}
}