Volume 17, Issue 6
Connection Between Grad-Div Stabilized Stokes Finite Elements and Divergence-Free Stokes Finite Elements

​Michael Neilan & Ahmed Zytoon

DOI:

Int. J. Numer. Anal. Mod., 17 (2020), pp. 839-857.

Published online: 2020-10

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  • Abstract

In this paper, we use recently developed theories of divergence–free finite element schemes to analyze methods for the Stokes problem with grad-div stabilization. For example, we show that, if the polynomial degree is sufficiently large, the solutions of the Taylor–Hood finite element scheme converges to an optimal convergence exactly divergence–free solution as the grad-div parameter tends to infinity. In addition, we introduce and analyze a stable first-order scheme that does not exhibit locking phenomenon for large grad-div parameters.

  • Keywords

Finite element methods, grad-div stabilization, divergence-free.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-17-839, author = {​Michael Neilan , and Ahmed Zytoon , }, title = {Connection Between Grad-Div Stabilized Stokes Finite Elements and Divergence-Free Stokes Finite Elements}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {6}, pages = {839--857}, abstract = {

In this paper, we use recently developed theories of divergence–free finite element schemes to analyze methods for the Stokes problem with grad-div stabilization. For example, we show that, if the polynomial degree is sufficiently large, the solutions of the Taylor–Hood finite element scheme converges to an optimal convergence exactly divergence–free solution as the grad-div parameter tends to infinity. In addition, we introduce and analyze a stable first-order scheme that does not exhibit locking phenomenon for large grad-div parameters.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/18354.html} }
TY - JOUR T1 - Connection Between Grad-Div Stabilized Stokes Finite Elements and Divergence-Free Stokes Finite Elements AU - ​Michael Neilan , AU - Ahmed Zytoon , JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 839 EP - 857 PY - 2020 DA - 2020/10 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/18354.html KW - Finite element methods, grad-div stabilization, divergence-free. AB -

In this paper, we use recently developed theories of divergence–free finite element schemes to analyze methods for the Stokes problem with grad-div stabilization. For example, we show that, if the polynomial degree is sufficiently large, the solutions of the Taylor–Hood finite element scheme converges to an optimal convergence exactly divergence–free solution as the grad-div parameter tends to infinity. In addition, we introduce and analyze a stable first-order scheme that does not exhibit locking phenomenon for large grad-div parameters.

​Michael Neilan & Ahmed Zytoon. (2020). Connection Between Grad-Div Stabilized Stokes Finite Elements and Divergence-Free Stokes Finite Elements. International Journal of Numerical Analysis and Modeling. 17 (6). 839-857. doi:
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