{"title":"再论周期性介质多尺度有限元法的误差估计","authors":"Pingbing Ming, Siqi Song","doi":"10.1137/22m1511060","DOIUrl":null,"url":null,"abstract":"Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 106-124, March 2024. <br/> Abstract. We derive the optimal energy error estimate for a multiscale finite element method with oversampling technique applied to an elliptic system with rapidly oscillating periodic coefficients under the assumption that the coefficients are bounded and measurable, which may admit rough microstructures. As a byproduct of the energy error estimate, we derive the rate of convergence in the [math]-norm.","PeriodicalId":501053,"journal":{"name":"Multiscale Modeling and Simulation","volume":"3 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Error Estimate of Multiscale Finite Element Method for Periodic Media Revisited\",\"authors\":\"Pingbing Ming, Siqi Song\",\"doi\":\"10.1137/22m1511060\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 106-124, March 2024. <br/> Abstract. We derive the optimal energy error estimate for a multiscale finite element method with oversampling technique applied to an elliptic system with rapidly oscillating periodic coefficients under the assumption that the coefficients are bounded and measurable, which may admit rough microstructures. As a byproduct of the energy error estimate, we derive the rate of convergence in the [math]-norm.\",\"PeriodicalId\":501053,\"journal\":{\"name\":\"Multiscale Modeling and Simulation\",\"volume\":\"3 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Multiscale Modeling and Simulation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/22m1511060\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Multiscale Modeling and Simulation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/22m1511060","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Error Estimate of Multiscale Finite Element Method for Periodic Media Revisited
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 106-124, March 2024. Abstract. We derive the optimal energy error estimate for a multiscale finite element method with oversampling technique applied to an elliptic system with rapidly oscillating periodic coefficients under the assumption that the coefficients are bounded and measurable, which may admit rough microstructures. As a byproduct of the energy error estimate, we derive the rate of convergence in the [math]-norm.
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