TY - JOUR
T1 - A Quadrilateral ‘Mini’ Finite Element for the Stokes Problem Using a Single Bubble Function
AU - Bishnu P. Lamichhane
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 - <p style="text-align: justify;">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.</p>