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

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

Authors: Thomas Lewis (The Univ. of North Carolina, Greensboro, NC, USA)
         Aaron Rapp (The Univ. of the Virgin Islands, St. Thomas, USA) 
         Yi Zhang  (The Univ. of North Carolina, Greensboro, NC, USA)
 
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.