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A quadrilateral 'mini' finite element for the Stokes problem using a single bubble function

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.

preprint2015arXivOpen access
Bishnu P. Lamichhane
math.NANumerical Analysis
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Bishnu P. Lamichhane

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