Continuous interior penalty stabilization for divergence-free finite element methods

Barrenechea, Gabriel R and Burman, Erik and Cáceres, Ernesto and Guzmán, Johnny (2023) Continuous interior penalty stabilization for divergence-free finite element methods. IMA Journal of Numerical Analysis. drad030. ISSN 0272-4979 (https://doi.org/10.1093/imanum/drad030)

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Abstract

In this paper, we propose, analyze and test numerically a pressure-robust stabilized finite element for a linearized problem in incompressible fluid mechanics, namely, the steady Oseen equation with low viscosity. Stabilization terms are defined by jumps of different combinations of derivatives for the convective term over the element faces of the triangulation of the domain. With the help of these stabilizing terms, and the fact the finite element space is assumed to provide a point-wise divergence-free velocity, an $\mathcal O\big(h^{k+\frac 12}\big)$ error estimate in the $L^2$-norm is proved for the method (in the convection-dominated regime), and optimal order estimates in the remaining norms of the error. Numerical results supporting the theoretical findings are provided.

ORCID iDs

Barrenechea, Gabriel R ORCID logoORCID: https://orcid.org/0000-0003-4490-678X, Burman, Erik, Cáceres, Ernesto and Guzmán, Johnny;
  • Item type:Article
    ID code:85831
    Dates:
    Date
    Event
    2 June 2023
    Published
    2 June 2023
    Published Online
    13 April 2023
    Accepted
    13 May 2022
    Submitted
    Keywords:Oseen equations, divergence-free mixed finite element methods, pressure robustness, convection stabilization, continuous interior penalty, Analysis, Numerical Analysis
    Subjects:Science > Mathematics > Analysis
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:19 Jun 2023 13:28
    Last modified:20 Jun 2023 00:48
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/85831
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