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Volume 14, Issue 6
A Quadrilateral ‘Mini’ Finite Element for the Stokes Problem Using a Single Bubble Function

Bishnu P. Lamichhane

Int. J. Numer. Anal. Mod., 14 (2017), pp. 869-878.

Published online: 2017-10

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  • Abstract

We consider a quadrilateral ‘mini’ finite element for approximating the solution of Stokes equations using a quadrilateral mesh. We use the standard bilinear finite element space enriched with element-wise defined bubble functions for the velocity and the standard bilinear finite element space for the pressure space. With a simple modification of the standard bubble function we show that a single bubble function is sufficient to ensure the inf-sup condition. We have thus improved an earlier result on the quadrilateral ‘mini’ element, where more than one bubble function are used to get the stability.

  • Keywords

Stokes equations, mixed finite elements, Mini finite element, inf-sup condition, bubble function.

  • AMS Subject Headings

65N30, 65N15, 74B10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-869, author = {Bishnu P. Lamichhane}, title = {A Quadrilateral ‘Mini’ Finite Element for the Stokes Problem Using a Single Bubble Function}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2017}, volume = {14}, number = {6}, pages = {869--878}, abstract = {

We consider a quadrilateral ‘mini’ finite element for approximating the solution of Stokes equations using a quadrilateral mesh. We use the standard bilinear finite element space enriched with element-wise defined bubble functions for the velocity and the standard bilinear finite element space for the pressure space. With a simple modification of the standard bubble function we show that a single bubble function is sufficient to ensure the inf-sup condition. We have thus improved an earlier result on the quadrilateral ‘mini’ element, where more than one bubble function are used to get the stability.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10484.html} }
TY - JOUR T1 - A Quadrilateral ‘Mini’ Finite Element for the Stokes Problem Using a Single Bubble Function AU - Bishnu P. Lamichhane JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 869 EP - 878 PY - 2017 DA - 2017/10 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10484.html KW - Stokes equations, mixed finite elements, Mini finite element, inf-sup condition, bubble function. AB -

We consider a quadrilateral ‘mini’ finite element for approximating the solution of Stokes equations using a quadrilateral mesh. We use the standard bilinear finite element space enriched with element-wise defined bubble functions for the velocity and the standard bilinear finite element space for the pressure space. With a simple modification of the standard bubble function we show that a single bubble function is sufficient to ensure the inf-sup condition. We have thus improved an earlier result on the quadrilateral ‘mini’ element, where more than one bubble function are used to get the stability.

Bishnu P. Lamichhane. (2017). A Quadrilateral ‘Mini’ Finite Element for the Stokes Problem Using a Single Bubble Function. International Journal of Numerical Analysis and Modeling. 14 (6). 869-878. doi:
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