On the stability of semi-Lagrangian advection schemes under finite element interpolation

We investigate about the stability of Semi-Lagrangian schemes when finite-element type reconstructions are used. This choice leads to a scheme whose stability cannot be characterized by means of the classical Fourier analysis. In the paper, we propose a technique to estimate eigenvalues of the scheme in the case of a uniform mesh, and extend it to some situation of non-uniform spacing. The explicit computation is carried out for the P2 case