A hybrid method for the inviscid Burgers equation

We describe a hybrid method for the numerical solution of the inviscid Burgers equation. The proposed scheme consists of a Fourier Galerkin spectral method for the resolution of the large scales of the solution coupled to a real space method capable of reproducing the small scale features such as shocks. The hybrid scheme captures correctly the decay of the energy of the solution. The underlying idea of the scheme fits in the optimal prediction framework where prior knowledge about an equation is used to improve upon existing algorithms.