Second order monotone finite differences discretization of linear anisotropic differential operators

We design adaptive finite differences discretizations, which are degenerate elliptic and second order consistent, of linear quasi-linear partial differential operators featuring both a first term ananisotropicsecond term. Our approach requires the domain to be discretized on Cartesian grid, takes advantage techniques from field low-dimensional lattice geometry. prove that stencil our numerical scheme is optimally compact, in dimension two, quasi-optimal terms compatibility condition required operators, dimensions two three. Numerical experiments illustrate efficiency method several contexts.