TY - JOUR T1 - A Quadrilateral ‘Mini’ Finite Element for the Stokes Problem Using a Single Bubble Function JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 869 EP - 878 PY - 2017 DA - 2017/10 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10484.html KW - Stokes equations, mixed finite elements, Mini finite element, inf-sup condition, bubble function. AB -

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.