{"title":"Morley type virtual element method for von Kármán equations","authors":"Devika Shylaja, Sarvesh Kumar","doi":"10.1007/s10444-024-10158-z","DOIUrl":null,"url":null,"abstract":"<div><p>This paper analyses the nonconforming Morley type virtual element method to approximate a regular solution to the von Kármán equations that describes bending of very thin elastic plates. Local existence and uniqueness of a discrete solution to the non-linear problem is discussed. A priori error estimate in the energy norm is established under minimal regularity assumptions on the exact solution. Error estimates in piecewise <span>\\(H^1\\)</span> and <span>\\(L^2\\)</span> norms are also derived. A working procedure to find an approximation for the discrete solution using Newton’s method is discussed. Numerical results that justify theoretical estimates are presented.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 5","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Computational Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10444-024-10158-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper analyses the nonconforming Morley type virtual element method to approximate a regular solution to the von Kármán equations that describes bending of very thin elastic plates. Local existence and uniqueness of a discrete solution to the non-linear problem is discussed. A priori error estimate in the energy norm is established under minimal regularity assumptions on the exact solution. Error estimates in piecewise \(H^1\) and \(L^2\) norms are also derived. A working procedure to find an approximation for the discrete solution using Newton’s method is discussed. Numerical results that justify theoretical estimates are presented.
期刊介绍：
Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis.
This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.
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