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A Finite Element Method for the Stokes Problem on Quadrilateral Grids Yielding Divergence Free Approximations

Sap, Duygu (2014) A Finite Element Method for the Stokes Problem on Quadrilateral Grids Yielding Divergence Free Approximations. Master's Thesis, University of Pittsburgh. (Unpublished)

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In this thesis project, a pair of conforming, stable and divergence free finite

elements for the Stokes problem on two dimensional rectangular grids with no-

slip boundary conditions is constructed. Pointwise continuous Q3,2 x Q2,3

polynomials that are partially C1 at the vertices and Q2,2 polynomials that

are continuous at the vertices are used as the functions forming the velocity and

pressure spaces, respectively. In the construction of these finite element spaces,

a Stokes complex is formed to verify the incompressibility of the velocity


With the definition of appropriate norms and the use of the Piola transform, the

inf-sup stability condition is satisfied on each rectangular element and then in

the entire domain. Furthermore, by applying Nitsche's method to the problem

and with the verification of the coercivity and continuity of the bilinear form, the

existence and the uniqueness of the solution to the Stokes problem is justified.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Sap, Duygudus8@pitt.eduDUS8
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairNeilan, Michaelneilan@pitt.eduNEILAN
Committee MemberYotov, Ivanyotov@math.pitt.eduYOTOV
Committee MemberLayton, Williamwjl@pitt.eduWJL
Date: 22 May 2014
Date Type: Publication
Defense Date: 17 April 2014
Approval Date: 22 May 2014
Submission Date: 5 May 2014
Access Restriction: 1 year -- Restrict access to University of Pittsburgh for a period of 1 year.
Number of Pages: 35
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: MS - Master of Science
Thesis Type: Master's Thesis
Refereed: Yes
Uncontrolled Keywords: finite element method, stokes, 2D, rectangular mesh
Date Deposited: 22 May 2014 20:14
Last Modified: 15 Nov 2016 14:20


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