Spectral element method: a simple example

Consider the 1D advection problem of a scalar \phi with constant velocity U=1:

\frac{\partial \phi}{\partial t} = - U \frac{\partial \phi}{\partial x}, \qquad -1 \le x \le 1, \qquad t > 0,

\phi(x,0) = e^{-ln(2)(x+1)^2/\sigma^2},

\phi(-1,t) = e^{-ln(2)(1-t)^2/\sigma^2},

where \sigma=0.2.

Fig.1 compares the convergence (norm 2 of the difference between the numerical and exact solution) of Discontinuous Galerkin Method and Finite Difference for the problem above.


Fig.1: Convergence of Discontinuos Galerkin Method (DG) and Finite difference (FD) for a 1D advection problem.


About Alexandre Fabregat Tomàs

As a postdoctoral fellow at City University of New York, I am interested in everything related with the numerical simulation of heat and mass transport in turbulent flows.
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