scholarly journals Analysis of Mixed Interior Penalty Discontinuous Galerkin Methods for the Cahn–Hilliard Equation and the Hele–Shaw Flow

2016 ◽  
Vol 54 (2) ◽  
pp. 825-847 ◽  
Author(s):  
Xiaobing Feng ◽  
Yukun Li ◽  
Yulong Xing
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Galerkin Methods ◽  
Interior Penalty ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

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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