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Volume 30, Issue 2
Grad-div Stabilized Finite Element Schemes for the Fluid-Fluid Interaction Model

Wei Li, Pengzhan Huang & Yinnian He

DOI: 10.4208/cicp.OA-2020-0123

Commun. Comput. Phys., 30 (2021), pp. 536-566.

Published online: 2021-05

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  • Abstract

In this work, two fully discrete grad-div stabilized finite element schemes for the fluid-fluid interaction model are considered. The first scheme is standard grad-div stabilized scheme, and the other one is modular grad-div stabilized scheme which adds to Euler backward scheme an update step and does not increase computational time for increasing stabilized parameters. Moreover, stability and error estimates of these schemes are given. Finally, computational tests are provided to verify both the numerical theory and efficiency of the presented schemes.

  • Keywords

Fluid-fluid interaction model, grad-div stabilized scheme, stability, error estimate.

  • AMS Subject Headings

65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-30-536, author = {Li , WeiHuang , Pengzhan and He , Yinnian}, title = {Grad-div Stabilized Finite Element Schemes for the Fluid-Fluid Interaction Model}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {2}, pages = {536--566}, abstract = {

In this work, two fully discrete grad-div stabilized finite element schemes for the fluid-fluid interaction model are considered. The first scheme is standard grad-div stabilized scheme, and the other one is modular grad-div stabilized scheme which adds to Euler backward scheme an update step and does not increase computational time for increasing stabilized parameters. Moreover, stability and error estimates of these schemes are given. Finally, computational tests are provided to verify both the numerical theory and efficiency of the presented schemes.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0123}, url = {http://global-sci.org/intro/article_detail/cicp/19124.html} }
TY - JOUR T1 - Grad-div Stabilized Finite Element Schemes for the Fluid-Fluid Interaction Model AU - Li , Wei AU - Huang , Pengzhan AU - He , Yinnian JO - Communications in Computational Physics VL - 2 SP - 536 EP - 566 PY - 2021 DA - 2021/05 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2020-0123 UR - https://global-sci.org/intro/article_detail/cicp/19124.html KW - Fluid-fluid interaction model, grad-div stabilized scheme, stability, error estimate. AB -

In this work, two fully discrete grad-div stabilized finite element schemes for the fluid-fluid interaction model are considered. The first scheme is standard grad-div stabilized scheme, and the other one is modular grad-div stabilized scheme which adds to Euler backward scheme an update step and does not increase computational time for increasing stabilized parameters. Moreover, stability and error estimates of these schemes are given. Finally, computational tests are provided to verify both the numerical theory and efficiency of the presented schemes.

Wei Li, Pengzhan Huang & Yinnian He. (2021). Grad-div Stabilized Finite Element Schemes for the Fluid-Fluid Interaction Model. Communications in Computational Physics. 30 (2). 536-566. doi:10.4208/cicp.OA-2020-0123
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