Connection Between Grad-Div Stabilized Stokes Finite Elements and Divergence-Free Stokes Finite Elements

Connection Between Grad-Div Stabilized Stokes Finite Elements and Divergence-Free Stokes Finite Elements

Year:    2020

Author:    Michael Neilan, Ahmed Zytoon

International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 6 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2020-IJNAM-18354

International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 6 : pp. 839–857

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Finite element methods grad-div stabilization divergence-free.

Author Details

Michael Neilan

Ahmed Zytoon