多孔介质中接触问题的后验误差估计

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications Pub Date : 2024-09-09 DOI:10.1016/j.camwa.2024.08.010

L. Banz , F. Bertrand

{"title":"多孔介质中接触问题的后验误差估计","authors":"L. Banz , F. Bertrand","doi":"10.1016/j.camwa.2024.08.010","DOIUrl":null,"url":null,"abstract":"<div><p>We present a family of generic a posteriori error estimators for the two-field Biot contact problem. While every family member of these estimators is reliable only certain members are also efficient. A crucial property of our error estimator is that it can measure the error of any approximation, not only of approximations with Galerkin orthogonality. Hence, it can be easily coupled with primal-dual active set algorithms. Additionally, we present explicitly an <em>hp</em>-finite element discretization and its residual based a posteriori error estimator based on the generic setup. Several numerical experiments underline the theoretical results.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A posteriori error estimate for contact problems in porous media\",\"authors\":\"L. Banz , F. Bertrand\",\"doi\":\"10.1016/j.camwa.2024.08.010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We present a family of generic a posteriori error estimators for the two-field Biot contact problem. While every family member of these estimators is reliable only certain members are also efficient. A crucial property of our error estimator is that it can measure the error of any approximation, not only of approximations with Galerkin orthogonality. Hence, it can be easily coupled with primal-dual active set algorithms. Additionally, we present explicitly an <em>hp</em>-finite element discretization and its residual based a posteriori error estimator based on the generic setup. Several numerical experiments underline the theoretical results.</p></div>\",\"PeriodicalId\":55218,\"journal\":{\"name\":\"Computers & Mathematics with Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-09-09\",\"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/S0898122124003572\",\"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/S0898122124003572","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

我们提出了双场 Biot 接触问题的一系列通用后验误差估计器。虽然这些估计器家族的每个成员都是可靠的，但只有某些成员是高效的。我们的误差估计器的一个重要特性是，它可以测量任何近似值的误差，而不仅仅是具有 Galerkin 正交性的近似值的误差。因此，它可以很容易地与原始二元主动集算法相结合。此外，我们还明确提出了基于通用设置的 hp 有限元离散化及其基于残差的后验误差估算器。几个数值实验证实了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A posteriori error estimate for contact problems in porous media

We present a family of generic a posteriori error estimators for the two-field Biot contact problem. While every family member of these estimators is reliable only certain members are also efficient. A crucial property of our error estimator is that it can measure the error of any approximation, not only of approximations with Galerkin orthogonality. Hence, it can be easily coupled with primal-dual active set algorithms. Additionally, we present explicitly an hp-finite element discretization and its residual based a posteriori error estimator based on the generic setup. Several numerical experiments underline the theoretical results.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Computers & Mathematics with Applications 工程技术-计算机：跨学科应用

CiteScore

5.10

自引率

10.30%

发文量

396

审稿时长

9.9 weeks

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).