Dissertation/Thesis Abstract

Symmetric Dual-Wind Discontinuous Galerkin Methods for Elliptic Variational Inequalities
by Rapp, Aaron Frost, Ph.D., The University of North Carolina at Greensboro, 2020, 209; 28001615
Abstract (Summary)

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.

Indexing (document details)
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
Subjects: Mathematics
Keywords: Discontinuous galerkin methods, Error estimates, Obstacle problem, Penalty parameter, Variational inequalities
Publication Number: 28001615
ISBN: 9798664797114
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