scholarly journals Multigrid algorithms for $$\varvec{hp}$$ h p -version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes

CALCOLO ◽  
2017 ◽  
Vol 54 (4) ◽  
pp. 1169-1198 ◽  
Author(s):  
P. F. Antonietti ◽  
P. Houston ◽  
X. Hu ◽  
M. Sarti ◽  
M. Verani
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Galerkin Methods ◽  
Interior Penalty ◽  
Polyhedral Meshes

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.

Discrete maximum principle for interior penalty discontinuous Galerkin methods

2013 ◽  
Vol 11 (4) ◽  
Author(s):  
Tamás Horváth ◽  
Miklós Mincsovics
Keyword(s):  
Maximum Principle ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Mesh Size ◽  
Discrete Maximum Principle ◽  
Galerkin Methods ◽  
Penalty Parameter ◽  
Discrete Level ◽  
Interior Penalty ◽  
Theoretical Results

AbstractA class of linear elliptic operators has an important qualitative property, the so-called maximum principle. In this paper we investigate how this property can be preserved on the discrete level when an interior penalty discontinuous Galerkin method is applied for the discretization of a 1D elliptic operator. We give mesh conditions for the symmetric and for the incomplete method that establish some connection between the mesh size and the penalty parameter. We then investigate the sharpness of these conditions. The theoretical results are illustrated with numerical examples.

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