Symmetric dual-wind discontinuous Galerkin methods for elliptic variational inequalities
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- Aaron Frost Rapp (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
- Advisor
- Thomas Lewis
Abstract: The main goal of this dissertation is to formulate and analyze a dual wind discontinuous Galerkin method for approximating solutions to elliptic variational inequalities. A discontinuous Galerkin (DG) finite-element interior calculus is used as a common framework to describe various DG approximation methods for second-order elliptic problems. The dual-wind discontinuous Galerkin method is formulated for the obstacle problem with Dirichlet boundary conditions, ??_u _ f on with u = g on @, u _ on , and (_u ?? f)(u ?? ) = 0 on . A complete convergence analysis is developed and numerical experiments are recorded that verify these results. A secondary goal of this dissertation is to explore the effect of the penalty parameter on the error of the dual-wind discontinuous Galerkin method’s approximation to an elliptic partial differential equation. The dual-wind discontinuous Galerkin method is applied to the Poisson problem in two dimensions. The dual-wind discontinuous Galerkin approximation to the Poisson problem is constructed using various penalty parameters and the error is recorded for each approximation across various initial meshes and their refinements. [This abstract has been edited to remove characters that will not display in this system. Please see the PDF for the full abstract.]
Symmetric dual-wind discontinuous Galerkin methods for elliptic variational inequalities
PDF (Portable Document Format)
17714 KB
Created on 8/1/2020
Views: 333
Additional Information
- Publication
- Dissertation
- Language: English
- Date: 2020
- Keywords
- Discontinuous Galerkin methods, Error Estimates, Obstacle Problem, Penalty Parameter, Variational Inequalities
- Subjects
- Galerkin methods
- Discontinuous functions
- Variational inequalities (Mathematics)