Numerical and theoretical discussions for solving nonlinear generalized Benjamin–Bona–Mahony–Burgers equation based on the Legendre spectral element method

2020 ◽  
Vol 37 (1) ◽  
pp. 360-382
Author(s):  
Mehdi Dehghan ◽  
Nasim Shafieeabyaneh ◽  
Mostafa Abbaszadeh
Keyword(s):  
Spectral Element Method ◽  
Burgers Equation ◽  
Spectral Element ◽  
Legendre Spectral Element Method ◽  
Element Method

A Space-Time Discontinuous Galerkin Spectral Element Method for Nonlinear Hyperbolic Problems

2018 ◽  
Vol 16 (01) ◽  
pp. 1850093 ◽  
Author(s):  
Chaoxu Pei ◽  
Mark Sussman ◽  
M. Yousuff Hussaini
Keyword(s):  
Discontinuous Galerkin ◽  
Spectral Element Method ◽  
Burgers Equation ◽  
Spectral Element ◽  
Space Time ◽  
Picard Iteration ◽  
Spectral Accuracy ◽  
Element Discretization ◽  
Space And Time ◽  
Element Method

A space-time discontinuous Galerkin spectral element method is combined with two different approaches for treating problems with discontinuous solutions: (i) adding a space-time dependent artificial viscosity, and (ii) tracking the discontinuity with space-time spectral accuracy. A Picard iteration method is employed to solve nonlinear system of equations derived from the space-time DG spectral element discretization. Spectral accuracy in both space and time is demonstrated for the Burgers’ equation with a smooth solution. For tests with discontinuities, the present space-time method enables better accuracy at capturing the shock strength in the element containing shock when higher order polynomials in both space and time are used. The spectral accuracy of the shock speed and location is demonstrated for the solution of the inviscid Burgers’ equation obtained by the tracking method.

A Fourier–Legendre spectral element method in polar coordinates

2012 ◽  
Vol 231 (2) ◽  
pp. 666-675 ◽  
Author(s):  
Zhouhua Qiu ◽  
Zhong Zeng ◽  
Huan Mei ◽  
Liang Li ◽  
Liping Yao ◽  
...  
Keyword(s):  
Spectral Element Method ◽  
Spectral Element ◽  
Polar Coordinates ◽  
Legendre Spectral Element Method ◽  
Element Method
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