Add to ORKGWe present a new integral representation for the flux of the advection-diffusion-reaction equation, which is based on the solution of a local boundary value problem for the entire equation, including the source term. The flux therefore consists of two parts, corresponding to the homogeneous and particular solution of the boundary value problem. Applying suitable quadrature rules to the integral representation gives the complete flux scheme, which is second order accurate, uniformly in the local Peclet numbers. The flux approximation is combined with a finite volume method, and the resulting finite volume-complete flux scheme is validated for several test problems