Spectral element method: a simple example

Posted on August 20, 2016 by Alexandre Fabregat Tomàs

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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