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)
The University of North Carolina at Greensboro (UNCG )
Web Site:
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.]

Additional Information

Language: English
Date: 2020
Discontinuous Galerkin methods, Error Estimates, Obstacle Problem, Penalty Parameter, Variational Inequalities
Galerkin methods
Discontinuous functions
Variational inequalities (Mathematics)

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