{"title":"用积分微分方程模拟动态分数阶粘弹性的混合应力有限元方法","authors":"Menghan Liu, Xiaoping Xie","doi":"10.4208/ijnam2024-1009","DOIUrl":null,"url":null,"abstract":"We consider a semi-discrete finite element method for a dynamic model for linear viscoelastic materials based on the constitutive law of fractional order. The corresponding\nintegro-differential equation is of a Mittag-Leffler type convolution kernel. A 4-node hybrid stress\nquadrilateral finite element is used for the spatial discretization. We show the existence and\nuniqueness of the semi-discrete solution, then derive some error estimates. Finally, we provide\nseveral numerical examples to verify the theoretical results.","PeriodicalId":50301,"journal":{"name":"International Journal of Numerical Analysis and Modeling","volume":"18 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Hybrid Stress Finite Element Method for Integro-Differential Equations Modelling Dynamic Fractional Order Viscoelasticity\",\"authors\":\"Menghan Liu, Xiaoping Xie\",\"doi\":\"10.4208/ijnam2024-1009\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a semi-discrete finite element method for a dynamic model for linear viscoelastic materials based on the constitutive law of fractional order. The corresponding\\nintegro-differential equation is of a Mittag-Leffler type convolution kernel. A 4-node hybrid stress\\nquadrilateral finite element is used for the spatial discretization. We show the existence and\\nuniqueness of the semi-discrete solution, then derive some error estimates. Finally, we provide\\nseveral numerical examples to verify the theoretical results.\",\"PeriodicalId\":50301,\"journal\":{\"name\":\"International Journal of Numerical Analysis and Modeling\",\"volume\":\"18 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Numerical Analysis and Modeling\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4208/ijnam2024-1009\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Numerical Analysis and Modeling","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/ijnam2024-1009","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A Hybrid Stress Finite Element Method for Integro-Differential Equations Modelling Dynamic Fractional Order Viscoelasticity
We consider a semi-discrete finite element method for a dynamic model for linear viscoelastic materials based on the constitutive law of fractional order. The corresponding
integro-differential equation is of a Mittag-Leffler type convolution kernel. A 4-node hybrid stress
quadrilateral finite element is used for the spatial discretization. We show the existence and
uniqueness of the semi-discrete solution, then derive some error estimates. Finally, we provide
several numerical examples to verify the theoretical results.
期刊介绍：
The journal is directed to the broad spectrum of researchers in numerical methods throughout science and engineering, and publishes high quality original papers in all fields of numerical analysis and mathematical modeling including: numerical differential equations, scientific computing, linear algebra, control, optimization, and related areas of engineering and scientific applications. The journal welcomes the contribution of original developments of numerical methods, mathematical analysis leading to better understanding of the existing algorithms, and applications of numerical techniques to real engineering and scientific problems. Rigorous studies of the convergence of algorithms, their accuracy and stability, and their computational complexity are appropriate for this journal. Papers addressing new numerical algorithms and techniques, demonstrating the potential of some novel ideas, describing experiments involving new models and simulations for practical problems are also suitable topics for the journal. The journal welcomes survey articles which summarize state of art knowledge and present open problems of particular numerical techniques and mathematical models.
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