{"title":"A rotational pressure-correction discontinuous Galerkin scheme for the Cahn-Hilliard-Darcy-Stokes system","authors":"Meiting Wang, Guang-an Zou, Jian Li","doi":"10.1007/s10444-024-10151-6","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is devoted to the numerical approximations of the Cahn-Hilliard-Darcy-Stokes system, which is a combination of the modified Cahn-Hilliard equation with the Darcy-Stokes equation. A novel discontinuous Galerkin pressure-correction scheme is proposed for solving the coupled system, which can achieve the desired level of linear, fully decoupled, and unconditionally energy stable. The developed scheme here is implemented by combining several effective techniques, including by adding an additional stabilization term artificially in Cahn-Hilliard equation for balancing the explicit treatment of the coupling term, the stabilizing strategy for the nonlinear energy potential, and a rotational pressure-correction scheme for the Darcy-Stokes equation. We rigorously prove the unique solvability, unconditional energy stability, and optimal error estimates of the proposed scheme. Finally, a number of numerical examples are provided to demonstrate numerically the efficiency of the present formulation.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Computational Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10444-024-10151-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is devoted to the numerical approximations of the Cahn-Hilliard-Darcy-Stokes system, which is a combination of the modified Cahn-Hilliard equation with the Darcy-Stokes equation. A novel discontinuous Galerkin pressure-correction scheme is proposed for solving the coupled system, which can achieve the desired level of linear, fully decoupled, and unconditionally energy stable. The developed scheme here is implemented by combining several effective techniques, including by adding an additional stabilization term artificially in Cahn-Hilliard equation for balancing the explicit treatment of the coupling term, the stabilizing strategy for the nonlinear energy potential, and a rotational pressure-correction scheme for the Darcy-Stokes equation. We rigorously prove the unique solvability, unconditional energy stability, and optimal error estimates of the proposed scheme. Finally, a number of numerical examples are provided to demonstrate numerically the efficiency of the present formulation.
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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