Adaptive Discontinuous Galerkin Methods on Polytopic Meshes

2016 ◽  
pp. 187-206 ◽  
Author(s):  
Joe Collis ◽  
Paul Houston
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Galerkin Methods

scholarly journals Stable Filtering Procedures for Nodal Discontinuous Galerkin Methods

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Jan Nordström ◽  
Andrew R. Winters
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Galerkin Methods ◽  
Theoretical Discussion ◽  
Numerical Tests ◽  
Dg Methods ◽  
Theoretical Results ◽  
Filtering Procedure

AbstractWe prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits that the DG approximation is constructed from polynomial basis functions and that integrals are approximated with high-order accurate Legendre–Gauss–Lobatto quadrature. The theoretical discussion re-contextualizes stable filtering results for finite difference methods into the DG setting. Numerical tests verify and validate the underlying theoretical results.

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