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Discrete Miranda-Talenti estimates and applications to linear and nonlinear PDEs

Wu, Mohan (2019) Discrete Miranda-Talenti estimates and applications to linear and nonlinear PDEs. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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In this thesis, we construct simple and convergent finite element methods for linear
and nonlinear elliptic differential equations in non-divergence form with discontinuous
coefficients. The methods are based on a discrete Miranda-Talenti estimate,
which relates the H2 semi-norm of piecewise polynomials with the L2 norm of its
Laplacian on convex domains. We develop a stability and convergence theory of the
proposed methods, and back up the theory with numerical experiments. Furthermore,
we construct a finite element method for the Monge-Ampere problem by using
an equivalent Hamilton-Jacobi-Bellman formulation.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Wu, Mohanwumohan0000@gmail.commow110000-0003-2070-1341
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairNeilan, Michaelneilan@pitt.eduneilan
Committee MemberLayton, Williamwjl@pitt.eduwjl
Committee MemberYotov, Ivanyotov@math.pitt.eduyotov
Committee MemberWalkington,
Date: 26 September 2019
Date Type: Publication
Defense Date: 25 July 2019
Approval Date: 26 September 2019
Submission Date: 8 August 2019
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 84
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: FEM
Date Deposited: 26 Sep 2019 13:46
Last Modified: 26 Sep 2019 13:46


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