2021 UNC Greensboro PDE Conference. Electron. J. Diff. Eqns., Conference 26 (2022), pp. 123-138.

Penalty parameter and dual-wind discontinuous Galerkin approximation methods for elliptic second order PDEs

Thomas Lewis, Aaron Rapp, Yi Zhang

Abstract:
This article analyzes the effect of the penalty parameter used in symmetric dual-wind discontinuous Galerkin (DWDG) methods for approximating second order elliptic partial differential equations (PDE). DWDG methods follow from the DG differential calculus framework that d efines discrete differential operators used to replace the continuous differential operators when discretizing a PDE. We establish the convergence of the DWDG approximation to a continuous Galerkin approximation as the penalty parameter tends towards infinity. We also test the influence of the regularity of the solution for elliptic second-order PDEs with regards to the relationship between the penalty parameter and the error for the DWDG approximation. Numerical experiments are provided to validate the theoretical results and to investigate the relationship between the penalty parameter and the L^2-error.

Published August 25, 2022.
Math Subject Classifications: 65N30, 65N99.
Key Words: Discontinuous Galerkin methods; DWDG methods; penalty parameter; Poisson problem.
DOI: https://doi.org/10.58997/ejde.conf.26.l1

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Thomas Lewis
Department of Mathematics and Statistics
The University of North Carolina at Greensboro
Greensboro, NC 27402, USA
email: tllewis3@uncg.edu
Aaron Rapp
Department of Mathematical Sciences
The University of the Virgin Islands
Charlotte Amalie West, St. Thomas, 00820
United States Virgin Islands
email: aaron.rapp@uvi.edu
Yi Zhang
Department of Mathematics and Statistics
The University of North Carolina at Greensboro
Greensboro, NC 27402, USA
email: y_zhang7@uncg.edu

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