A Quadrilateral ‘Mini’ Finite Element for the Stokes Problem Using a Single Bubble Function

Volume 14, Issue 6

Bishnu P. Lamichhane

DOI:

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

Published online: 2017-10

Preview Purchase PDF 1 1881

Export citation

Cited by

google scholar semantic scholar

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 suffcient 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.

Email address

BibTex
RIS
TXT

@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 suffcient 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 KW - mixed finite elements KW - Mini finite element KW - inf-sup condition KW - 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 suffcient 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. (1970). 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:

Copy to clipboard

BibteX RIS TXT

The citation has been copied to your clipboard