{"title":"多边形网格上孔隙-弹性力学模型的混合虚拟元素方法","authors":"Yanli Chen , Xin Liu , Wenhui Zhang , Yufeng Nie","doi":"10.1016/j.camwa.2024.09.025","DOIUrl":null,"url":null,"abstract":"<div><div>This work introduces and analyzes the mixed virtual element method on polygonal meshes for the numerical discretization of poro-elastodynamics models. For spatial discretization, we employ the mixed virtual element method on polygonal meshes, coupled with Newmark-<em>β</em> integration schemes for time discretization. We present a stability analysis for both the continuous and semi-discrete problems and derive error estimates for the energy norm in the semi-discrete case. Numerical experiments are conducted to verify the theoretical analysis, and the results on Voronoi meshes demonstrate that the algorithm effectively handles various dynamic viscosities.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mixed virtual element methods for the poro-elastodynamics model on polygonal grids\",\"authors\":\"Yanli Chen , Xin Liu , Wenhui Zhang , Yufeng Nie\",\"doi\":\"10.1016/j.camwa.2024.09.025\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This work introduces and analyzes the mixed virtual element method on polygonal meshes for the numerical discretization of poro-elastodynamics models. For spatial discretization, we employ the mixed virtual element method on polygonal meshes, coupled with Newmark-<em>β</em> integration schemes for time discretization. We present a stability analysis for both the continuous and semi-discrete problems and derive error estimates for the energy norm in the semi-discrete case. Numerical experiments are conducted to verify the theoretical analysis, and the results on Voronoi meshes demonstrate that the algorithm effectively handles various dynamic viscosities.</div></div>\",\"PeriodicalId\":55218,\"journal\":{\"name\":\"Computers & Mathematics with Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-10-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computers & Mathematics with Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0898122124004334\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Mathematics with Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0898122124004334","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Mixed virtual element methods for the poro-elastodynamics model on polygonal grids
This work introduces and analyzes the mixed virtual element method on polygonal meshes for the numerical discretization of poro-elastodynamics models. For spatial discretization, we employ the mixed virtual element method on polygonal meshes, coupled with Newmark-β integration schemes for time discretization. We present a stability analysis for both the continuous and semi-discrete problems and derive error estimates for the energy norm in the semi-discrete case. Numerical experiments are conducted to verify the theoretical analysis, and the results on Voronoi meshes demonstrate that the algorithm effectively handles various dynamic viscosities.
期刊介绍:
Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).