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
Show me the PDF file (648 K), TEX file for this article.
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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 |
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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 |
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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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