scholarly journals A posteriorierror estimates for discontinuous Galerkin methods using non-polynomial basis functions. Part II: Eigenvalue problems

2017 ◽  
Vol 51 (5) ◽  
pp. 1733-1753 ◽  
Author(s):  
Lin Lin ◽  
Benjamin Stamm
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Eigenvalue Problems ◽  
Basis Functions ◽  
Polynomial Basis ◽  
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.

scholarly journals Layer-Wise Discontinuous Galerkin Methods for Piezoelectric Laminates

Modelling ◽  
2020 ◽  
Vol 1 (2) ◽  
pp. 198-214
Author(s):  
Ivano Benedetti ◽  
Vincenzo Gulizzi ◽  
Alberto Milazzo
Keyword(s):  
Discontinuous Galerkin ◽  
Electric Potential ◽  
Discontinuous Galerkin Methods ◽  
Basis Functions ◽  
Variable Order ◽  
Test Cases ◽  
Galerkin Methods ◽  
Computational Tool ◽  
Interior Penalty ◽  
Analysis And Design

In this work, a novel high-order formulation for multilayered piezoelectric plates based on the combination of variable-order interior penalty discontinuous Galerkin methods and general layer-wise plate theories is presented, implemented and tested. The key feature of the formulation is the possibility to tune the order of the basis functions in both the in-plane approximation and the through-the-thickness expansion of the primary variables, namely displacements and electric potential. The results obtained from the application to the considered test cases show accuracy and robustness, thus confirming the developed technique as a supplementary computational tool for the analysis and design of smart laminated devices.

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