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

Title: A quadrilateral 'mini' finite element for the stokes problem using a single bubble function
Creator: Lamichhane, Bishnu P.
Relation: International Journal of Numerical Analysis and Modeling Vol. 14, Issue 6, p. 869-878
Relation: http://www.math.ualberta.ca/ijnam/Volume14.htm
Publisher: University of Alberta, Department of Mathematical & Statistical Sciences
Resource Type: journal article
Date: 2017
Description: 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.
Subject: Stokes equations; mixed finite elements; mini finite element; inf-sup condition; bubble function
Identifier: http://hdl.handle.net/1959.13/1350137
Identifier: uon:30498
Identifier: ISSN:1705-5105
Language: eng
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