Interpolation of the divergence

I have a prescribed velocity field on a uniform, collocated 2D grid. I need to compute the divergence of the velocity field at some arbitrary points that does not coincide with the grid points or midpoint location.

On posibility could be to compute the divergence on the grid points and then interpolate using bicubic interpolation at the unknown points. I am not sure this is a good idea because it could create some checkerboard effect.

I wonder if there is a better way to do that.

Answer 1

[Mischa Kim]

Since it is probably more challenging to find a good data fit for derivatives of data, I would start with interpolating the velocity field. As a second step I would then compute the divergence of the interpolated data. To improve data quality you might also want to consider segmenting your 2D region.