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

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