{"title":"Local spline projectors of analysis-suitable T-splines","authors":"Hailun Xu, Hongmei Kang","doi":"10.1016/j.cam.2024.116484","DOIUrl":null,"url":null,"abstract":"<div><div>Quasi-interpolation based on analysis-suitable T-splines (AS T-splines) has been considered by Kang et al. (2022), but the provided method is only able to reproduce polynomial spaces. In this paper, we consider quasi-interpolation constructed from the local tensor product of linear functionals in univariate B-spline projectors. Thanks to the dual-compatibility property of AS T-splines, such quasi-interpolation leads to AS T-spline projectors. For practical applications, we provide explicit expressions and norm estimates for the projections of quadratic and cubic AS T-splines. We also present a comparison between the proposed AS T-spline projectors and several existing AS T-spline quasi-interpolations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"462 ","pages":"Article 116484"},"PeriodicalIF":2.1000,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724007325","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Quasi-interpolation based on analysis-suitable T-splines (AS T-splines) has been considered by Kang et al. (2022), but the provided method is only able to reproduce polynomial spaces. In this paper, we consider quasi-interpolation constructed from the local tensor product of linear functionals in univariate B-spline projectors. Thanks to the dual-compatibility property of AS T-splines, such quasi-interpolation leads to AS T-spline projectors. For practical applications, we provide explicit expressions and norm estimates for the projections of quadratic and cubic AS T-splines. We also present a comparison between the proposed AS T-spline projectors and several existing AS T-spline quasi-interpolations.
期刊介绍：
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.
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