scholarly journals A space-time discontinuous Galerkin spectral element method for the Stefan problem

2018 ◽  
Vol 23 (9) ◽  
pp. 3595-3622 ◽  
Author(s):  
Chaoxu Pei ◽  
◽  
Mark Sussman ◽  
M. Yousuff Hussaini
Keyword(s):  
Discontinuous Galerkin ◽  
Stefan Problem ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Space Time ◽  
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.

An Efficient High Performance Parallelization of a Discontinuous Galerkin Spectral Element Method

2013 ◽  
pp. 37-47 ◽  
Author(s):  
Christoph Altmann ◽  
Andrea D. Beck ◽  
Florian Hindenlang ◽  
Marc Staudenmaier ◽  
Gregor J. Gassner ◽  
...  
Keyword(s):  
Discontinuous Galerkin ◽  
High Performance ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Element Method

scholarly journals Space-time spectral element method solution for the acoustic wave equation and its dispersion analysis

2017 ◽  
Vol 38 (6) ◽  
pp. 303-313 ◽  
Author(s):  
Yanhui Geng ◽  
Guoliang Qin ◽  
Jiazhong Zhang ◽  
Wenqiang He ◽  
Zhenzhong Bao ◽  
...  
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Dispersion Analysis ◽  
Space Time ◽  
Acoustic Wave Equation ◽  
Element Method
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