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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 |
Source Type: | DISSERTATION |
Subjects: | Mathematics |
Keywords: | Discontinuous galerkin methods, Error estimates, Obstacle problem, Penalty parameter, Variational inequalities |
Publication Number: | 28001615 |
ISBN: | 9798664797114 |