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
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.
