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A quadrilateral 'mini' finite element for the Stokes problem using a single bubble function (1507.04417v1)
Published 16 Jul 2015 in cs.NA and math.NA
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.