Stabilized Spectral Element Approximation of the Saint Venant System Using the Entropy Viscosity Technique

2015 ◽  
pp. 397-404
Author(s):  
R. Pasquetti ◽  
J. L. Guermond ◽  
B. Popov
Keyword(s):  
Spectral Element ◽  
Element Approximation ◽  
Entropy Viscosity

scholarly journals A provably stable discontinuous Galerkin spectral element approximation for moving hexahedral meshes

2016 ◽  
Vol 139 ◽  
pp. 148-160 ◽  
Author(s):  
David A. Kopriva ◽  
Andrew R. Winters ◽  
Marvin Bohm ◽  
Gregor J. Gassner
Keyword(s):  
Discontinuous Galerkin ◽  
Spectral Element ◽  
Element Approximation ◽  
Hexahedral Meshes

SPECTRAL ELEMENT METHOD FOR ACOUSTIC PROPAGATION PROBLEMS BASED ON LINEARIZED EULER EQUATIONS

2009 ◽  
Vol 17 (04) ◽  
pp. 383-402 ◽  
Author(s):  
RONGXIN ZHANG ◽  
GUOLIANG QIN ◽  
CHANGYUN ZHU
Keyword(s):  
Euler Equations ◽  
Sound Propagation ◽  
Spectral Element ◽  
Acoustic Propagation ◽  
Absorbing Boundary Conditions ◽  
Element Approximation ◽  
Newmark Method ◽  
Mean Flow ◽  
Linearized Euler Equations ◽  
Accuracy And Stability

A Chebyshev spectral element approximation of acoustic propagation problems based on linearized Euler equations is introduced, and the numerical approach is based on spectral elements in space with first-order Clayton–Engquist–Majda absorbing boundary conditions and implicit Newmark method in time. An initial perturbation problem has been solved to test the accuracy and stability of the numerical method. Then the sound propagation by source terms is also studied, including the radiation of a monopole and dipolar source in both stationary medium and uniform mean flow. The numerical simulation leads to good results in both accuracy and stability. Compared with the analytical solutions, the numerical results show the advantages in spectral accuracy even with relatively fewer grid points. Moreover, the implicit Newmark method in time marching also presents its superiority in stability. Finally, a problem of sound propagation in pipes is simulated as well.

The Spectral Element Method for the Steklov Eigenvalue Problem

2013 ◽  
Vol 853 ◽  
pp. 631-635 ◽  
Author(s):  
Yan Jun Li ◽  
Yi Du Yang ◽  
Hai Bi
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Element Method ◽  
A Priori ◽  
Spectral Element ◽  
Element Approximation ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem ◽  
Priori Error Estimates ◽  
Shaped Domain ◽  
Element Method

This paper discusses the spectral element approximation with LGL node basis for the Steklov eigenvalue problem, and analyzes the a priori error estimates. Finally, numerical experi-ments on the square and the L-shaped domain are carried out to get very accurate approximations by the spectral element method.

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