A quadrilateral 'mini' finite element for the Stokes problem using a single bubble function
This work provides a more efficient finite element method for solving Stokes equations on quadrilateral meshes, benefiting computational fluid dynamics researchers.
The paper introduces a quadrilateral 'mini' finite element for the Stokes problem that requires only a single bubble function to satisfy the inf-sup condition, improving upon previous methods that used multiple bubble functions.
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.