Mimetic operators are approximations that satisfy discrete versions of continuum conservation laws and are used for finding numerical solutions of partial differential equations (PDE's). A technique for constructing mimetic schemes over non-uniform, structured, two-dimensional meshes is proposed. We construct divergence, gradient, curl, and boundary operators based on the application of local transformations and show how to use them for solving PDE's with general boundary conditions. Finally, a numerical convergence analysis is presented by solving a boundary layer like problem over different kind of meshes.