Narrow-stencil finite difference methods for linear second order elliptic problems of non-divergence form
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- Kellie Marie Ward (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
- Advisor
- Thomas Lewis
Abstract: This thesis presents a class of narrow-stencil finite difference methods for approximating the viscosity solution of second-order linear elliptic Dirichlet boundary value problems. The methods are simple to motivate and implement. This thesis proves admissibility and stability results for the simple narrow-stencil finite difference methods as well as optimal convergence rates when the underlying solution to the partial differential equation (PDE) is sufficiently smooth. The results in this thesis extend the analytic techniques first developed by Feng and Lewis when approximating viscosity solutions of fully nonlinear elliptic PDEs using the Lax-Friedrich’s-like method. Numerical tests are presented to gauge the performance of the methods and to validate the convergence results of the thesis.
Narrow-stencil finite difference methods for linear second order elliptic problems of non-divergence form
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Created on 12/1/2021
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Additional Information
- Publication
- Thesis
- Language: English
- Date: 2021
- Keywords
- Finite Difference methods, Hamilton-Jacobi-Bellman equations, Narrow-Stencil, Non-Divergence Form, Numerical moment, Viscosity
- Subjects
- Finite differences
- Viscosity solutions
- Dirichlet problem
- Differential equations, Elliptic