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research-article

An embedded–hybridized discontinuous Galerkin method for the coupled Stokes–Darcy system

Authors:

Aycil Cesmelioglu,

Sander Rhebergen,

Garth N. WellsAuthors Info & Claims

Volume 367, Issue C

https://doi.org/10.1016/j.cam.2019.112476

Published: 15 March 2020 Publication History

Abstract

We introduce an embedded–hybridized discontinuous Galerkin (EDG–HDG) method for the coupled Stokes–Darcy system. This EDG–HDG method is a pointwise mass-conserving discretization resulting in a divergence-conforming velocity field on the whole domain. In the proposed scheme, coupling between the Stokes and Darcy domains is achieved naturally through the EDG–HDG facet variables. A priori error analysis shows optimal convergence rates, and that the velocity error does not depend on the pressure. The error analysis is verified through numerical examples on unstructured grids for different orders of polynomial approximation.

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Cited By

Cesmelioglu ALee JRhebergen STabaku D(2024)A hybridizable discontinuous Galerkin method for the dual-porosity-Stokes problemComputers & Mathematics with Applications10.1016/j.camwa.2024.04.004165:C(180-195)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1016/j.camwa.2024.04.004
Lv DRui H(2024)Pressure-robust finite element scheme for the time-dependent fully coupled Stokes–Darcy-transport problemJournal of Computational and Applied Mathematics10.1016/j.cam.2024.116089451:COnline publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1016/j.cam.2024.116089
Wen JChen ZHe Y(2023)The analogue of grad-div stabilization in DG method for a coupled Stokes and Darcy problemComputers & Mathematics with Applications10.1016/j.camwa.2023.08.029149:C(99-114)Online publication date: 1-Nov-2023
https://dl.acm.org/doi/10.1016/j.camwa.2023.08.029
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An embedded–hybridized discontinuous Galerkin method for the coupled Stokes–Darcy system

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Published In

cover image Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics Volume 367, Issue C

Mar 2020

577 pages

ISSN:0377-0427

Issue’s Table of Contents

Elsevier B.V.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 15 March 2020

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Cited By

Cesmelioglu ALee JRhebergen STabaku D(2024)A hybridizable discontinuous Galerkin method for the dual-porosity-Stokes problemComputers & Mathematics with Applications10.1016/j.camwa.2024.04.004165:C(180-195)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1016/j.camwa.2024.04.004
Lv DRui H(2024)Pressure-robust finite element scheme for the time-dependent fully coupled Stokes–Darcy-transport problemJournal of Computational and Applied Mathematics10.1016/j.cam.2024.116089451:COnline publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1016/j.cam.2024.116089
Wen JChen ZHe Y(2023)The analogue of grad-div stabilization in DG method for a coupled Stokes and Darcy problemComputers & Mathematics with Applications10.1016/j.camwa.2023.08.029149:C(99-114)Online publication date: 1-Nov-2023
https://dl.acm.org/doi/10.1016/j.camwa.2023.08.029
Cesmelioglu ALee JRhebergen S(2023)Hybridizable discontinuous Galerkin methods for the coupled Stokes–Biot problemComputers & Mathematics with Applications10.1016/j.camwa.2023.05.024144:C(12-33)Online publication date: 15-Aug-2023
https://dl.acm.org/doi/10.1016/j.camwa.2023.05.024
Cesmelioglu ARhebergen S(2023)A hybridizable discontinuous Galerkin method for the coupled Navier–Stokes and Darcy problemJournal of Computational and Applied Mathematics10.1016/j.cam.2022.114923422:COnline publication date: 1-Apr-2023
https://dl.acm.org/doi/10.1016/j.cam.2022.114923
Cesmelioglu ALee JRhebergen S(2023)Analysis of an Embedded-Hybridizable Discontinuous Galerkin Method for Biot’s Consolidation ModelJournal of Scientific Computing10.1007/s10915-023-02373-597:3Online publication date: 24-Oct-2023
https://dl.acm.org/doi/10.1007/s10915-023-02373-5

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