{"title":"verfurt h误差估计器对亥姆霍兹方程EF解的有效性","authors":"Simona Iremie, Philippe Bouillard","doi":"10.1016/S1287-4620(00)88418-5","DOIUrl":null,"url":null,"abstract":"<div><p>The finite element solution of Helmholtz equation is dispersive and the existent a posteriori error estimators underestimate the pollution error implied by this phenomenon. In this paper, a new type of residual estimator for the Helmholtz operator is proposed and tested on a one-dimensional model problem. The numerical results show that the error is correctly estimated but new difficulties appear in the exact evaluation of problem dependent constants.</p></div>","PeriodicalId":100303,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy","volume":"328 1","pages":"Pages 67-71"},"PeriodicalIF":0.0000,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1287-4620(00)88418-5","citationCount":"0","resultStr":"{\"title\":\"Efficacité de l'estimateur d'erreur de Verfürt h pour la solution EF de l'équation de Helmholtz\",\"authors\":\"Simona Iremie, Philippe Bouillard\",\"doi\":\"10.1016/S1287-4620(00)88418-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The finite element solution of Helmholtz equation is dispersive and the existent a posteriori error estimators underestimate the pollution error implied by this phenomenon. In this paper, a new type of residual estimator for the Helmholtz operator is proposed and tested on a one-dimensional model problem. The numerical results show that the error is correctly estimated but new difficulties appear in the exact evaluation of problem dependent constants.</p></div>\",\"PeriodicalId\":100303,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy\",\"volume\":\"328 1\",\"pages\":\"Pages 67-71\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2000-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S1287-4620(00)88418-5\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1287462000884185\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1287462000884185","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Efficacité de l'estimateur d'erreur de Verfürt h pour la solution EF de l'équation de Helmholtz
The finite element solution of Helmholtz equation is dispersive and the existent a posteriori error estimators underestimate the pollution error implied by this phenomenon. In this paper, a new type of residual estimator for the Helmholtz operator is proposed and tested on a one-dimensional model problem. The numerical results show that the error is correctly estimated but new difficulties appear in the exact evaluation of problem dependent constants.
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