Wu, Mohan
(2019)
Discrete Miranda-Talenti estimates and applications to linear and nonlinear PDEs.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
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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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
|
| 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 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/37334 |
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