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CONVERGENCE ANALYSIS OF FINITE ELEMENT METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS IN NON-DIVERGENCE FORM

Hennings, Lauren (2014) CONVERGENCE ANALYSIS OF FINITE ELEMENT METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS IN NON-DIVERGENCE FORM. Master's Thesis, University of Pittsburgh. (Unpublished)

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Abstract

The purpose of this project is to derive stability estimates for a finite element method for linear, elliptic partial differential equation in non-divergence form. The thesis begins by introducing basic definitions of the Sobolev spaces used and the corresponding norms of these spaces. We then define the finite element method of the problem. We dedicate one chapter to working out what the finite element method reduces to when we are in one dimension. Chapter 4 involves preliminary lemmas which we will lead up to the proof of the main result. The proof of these lemmas, including the main result, involve a common theme of using inverse estimates, interpolation estimates, and various other inequalities. Once we prove the main result, we then prove existence, uniqueness, and error estimates of the solution of the finite element method. The last chapter is dedicated to numerical experiments. We choose three test problems in the one dimensional case and discuss error and convergence rates of each, as well as whether each problem supports the theoretical estimates.

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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Hennings, Lauren lnh31@pitt.eduLNH31
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairNeilan, Michaelneilan@pitt.eduNEILAN
Committee MemberLayton, Williamwjl@pitt.eduWJL
Committee MemberSati, Hishamhsati@pitt.eduHSATI
Date: 9 September 2014
Date Type: Publication
Defense Date: 17 April 2014
Approval Date: 9 September 2014
Submission Date: 27 March 2014
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 49
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: elliptic partial differential equations, stability estimates, finite element method
Date Deposited: 09 Sep 2014 22:16
Last Modified: 15 Nov 2016 14:19
URI: http://d-scholarship.pitt.edu/id/eprint/21275

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  • CONVERGENCE ANALYSIS OF FINITE ELEMENT METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS IN NON-DIVERGENCE FORM. (deposited 09 Sep 2014 22:16) [Currently Displayed]

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