On the implementation of discontinuous Galerkin methods for Volterra integral equations with highly oscillatory Bessel kernels

2013 ◽  
Vol 219 (9) ◽  
pp. 4884-4891 ◽  
Author(s):  
Shuhuang Xiang ◽  
Kaixian He
Keyword(s):  
Integral Equations ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Volterra Integral Equations ◽  
Galerkin Methods ◽  
Highly Oscillatory

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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