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

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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 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.

  • History

Published online: 2017-10

  • AMS Subject Headings

65N30, 65N15, 74B10.

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