Hey, i'am currently trying to make a stability analysis of a binary fluid at its phase border. As the governing equations in this double-diffusive problem are rather complicated i have to do a series expansion of my density profile. My problem is, that my PDEs contain a hevyside step function right at the border and i want to do a fourier expansion (i can then use symmetries of my problem and do some horrible algebra to actually get a "solution" which can be computed for up to 5 or 6 modes).

Now i know that fourier expansion performs quite horribly at a discontinous jump if only the first few modes are kept. Is it nervertheless possible to obtain a "margin of error"? Numerical precision is not of utmost concern, but the physics behind my problem should not all be thrown out by such an expansion. Do you know of any criteria or "better" expansion where its possible to make heavy use of symmetry/antisymmetry?

all the best, jan