Gradient and smoothing stencils with isotropic discretization error

Gradient stencils with isotropic O(h^2) and O(h^4) discretization error are constructed by considering their effect on common, rotationally invariant building blocks of field-theoretic Lagrangians in three dimensions. The same approach is then used to derive low-pass filters with isotropic O(h^4) and O(h^6) error.