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 ≥ ƒ on Ω with u = g on ∂Ω, u ≥ ψ on Ω, and (-∆u − ƒ)(u − ψ) = 0 on Ω. 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.
|Advisor:||Lewis, Tom, Zhang, Yi|
|Commitee:||Chhetri, Maya, Fabiano, Richard|
|School:||The University of North Carolina at Greensboro|
|Department:||College of Arts & Sciences: Mathematics and Statistics|
|School Location:||United States -- North Carolina|
|Source:||DAI-B 82/3(E), Dissertation Abstracts International|
|Keywords:||Discontinuous galerkin methods, Error estimates, Obstacle problem, Penalty parameter, Variational inequalities|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be