{"title":"含二次声的膨胀多孔热弹性介质的数值研究","authors":"A. Smouk, A. Radid, A. Soufyane","doi":"10.23939/mmc2023.03.772","DOIUrl":null,"url":null,"abstract":"In this work, we numerically consider a swelling porous thermoelastic system with a heat flux given by the Maxwell–Cattaneo law. We study the numerical energy and the exponential decay of the thermoelastic problem. First, we give a variational formulation written in terms of the transformed derivatives corresponding to a coupled linear system composed of four first-order variational equations. A fully discrete algorithm is introduced and a discrete stability property is proven. A priori error estimates are also provided. Finally, some numerical results are given to demonstrate the behavior of the solution.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A numerical study of swelling porous thermoelastic media with second sound\",\"authors\":\"A. Smouk, A. Radid, A. Soufyane\",\"doi\":\"10.23939/mmc2023.03.772\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, we numerically consider a swelling porous thermoelastic system with a heat flux given by the Maxwell–Cattaneo law. We study the numerical energy and the exponential decay of the thermoelastic problem. First, we give a variational formulation written in terms of the transformed derivatives corresponding to a coupled linear system composed of four first-order variational equations. A fully discrete algorithm is introduced and a discrete stability property is proven. A priori error estimates are also provided. Finally, some numerical results are given to demonstrate the behavior of the solution.\",\"PeriodicalId\":37156,\"journal\":{\"name\":\"Mathematical Modeling and Computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Modeling and Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.23939/mmc2023.03.772\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Modeling and Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23939/mmc2023.03.772","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
A numerical study of swelling porous thermoelastic media with second sound
In this work, we numerically consider a swelling porous thermoelastic system with a heat flux given by the Maxwell–Cattaneo law. We study the numerical energy and the exponential decay of the thermoelastic problem. First, we give a variational formulation written in terms of the transformed derivatives corresponding to a coupled linear system composed of four first-order variational equations. A fully discrete algorithm is introduced and a discrete stability property is proven. A priori error estimates are also provided. Finally, some numerical results are given to demonstrate the behavior of the solution.