{"title":"具有 Tresca 边界条件的斯托克斯流的非连续 Galerkin 方案：迭代后验误差分析","authors":"J.K. Djoko, T. Sayah","doi":"10.1007/s10444-024-10207-7","DOIUrl":null,"url":null,"abstract":"<div><p>In two dimensions, we propose and analyse an iterative <i>a posteriori</i> error indicator for the discontinuous Galerkin finite element approximations of the Stokes equations under boundary conditions of friction type. Two sources of error are identified here, namely; the discretisation error and the linearization error. Under a smallness assumption on data, we prove that the devised error estimator is reliable. Balancing these two errors is crucial to design an adaptive strategy for mesh refinement. We illustrate the theory with some representative numerical examples.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 6","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10207-7.pdf","citationCount":"0","resultStr":"{\"title\":\"Discontinuous Galerkin schemes for Stokes flow with Tresca boundary condition: iterative a posteriori error analysis\",\"authors\":\"J.K. Djoko, T. Sayah\",\"doi\":\"10.1007/s10444-024-10207-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In two dimensions, we propose and analyse an iterative <i>a posteriori</i> error indicator for the discontinuous Galerkin finite element approximations of the Stokes equations under boundary conditions of friction type. Two sources of error are identified here, namely; the discretisation error and the linearization error. Under a smallness assumption on data, we prove that the devised error estimator is reliable. Balancing these two errors is crucial to design an adaptive strategy for mesh refinement. We illustrate the theory with some representative numerical examples.</p></div>\",\"PeriodicalId\":50869,\"journal\":{\"name\":\"Advances in Computational Mathematics\",\"volume\":\"50 6\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-11-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10444-024-10207-7.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Computational Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10444-024-10207-7\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Computational Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10444-024-10207-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Discontinuous Galerkin schemes for Stokes flow with Tresca boundary condition: iterative a posteriori error analysis
In two dimensions, we propose and analyse an iterative a posteriori error indicator for the discontinuous Galerkin finite element approximations of the Stokes equations under boundary conditions of friction type. Two sources of error are identified here, namely; the discretisation error and the linearization error. Under a smallness assumption on data, we prove that the devised error estimator is reliable. Balancing these two errors is crucial to design an adaptive strategy for mesh refinement. We illustrate the theory with some representative numerical examples.
期刊介绍：
Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis.
This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.
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