{"title":"Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition","authors":"Hiroki Ishizaka","doi":"10.21136/AM.2024.0103-24","DOIUrl":null,"url":null,"abstract":"<div><p>We present a precise anisotropic interpolation error estimate for the Morley finite element method (FEM) and apply it to fourth-order elliptic equations. We do not impose the shape-regularity mesh condition in the analysis. Anisotropic meshes can be used for this purpose. The main contributions of this study include providing a new proof of the term consistency. This enables us to obtain an anisotropic consistency error estimate. The core idea of the proof involves using the relationship between the Raviart-Thomas and Morley finite-element spaces. Our results indicate optimal convergence rates and imply that the modified Morley FEM may be effective for errors.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 6","pages":"769 - 805"},"PeriodicalIF":0.6000,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applications of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.21136/AM.2024.0103-24","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We present a precise anisotropic interpolation error estimate for the Morley finite element method (FEM) and apply it to fourth-order elliptic equations. We do not impose the shape-regularity mesh condition in the analysis. Anisotropic meshes can be used for this purpose. The main contributions of this study include providing a new proof of the term consistency. This enables us to obtain an anisotropic consistency error estimate. The core idea of the proof involves using the relationship between the Raviart-Thomas and Morley finite-element spaces. Our results indicate optimal convergence rates and imply that the modified Morley FEM may be effective for errors.
期刊介绍：
Applications of Mathematics publishes original high quality research papers that are directed towards applications of mathematical methods in various branches of science and engineering.
The main topics covered include:
- Mechanics of Solids;
- Fluid Mechanics;
- Electrical Engineering;
- Solutions of Differential and Integral Equations;
- Mathematical Physics;
- Optimization;
- Probability
Mathematical Statistics.
The journal is of interest to a wide audience of mathematicians, scientists and engineers concerned with the development of scientific computing, mathematical statistics and applicable mathematics in general.
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