<p>This work investigates the application of Richardson Extrapolation (RE) and its variants, including the Repeated Richardson Extrapolation (RRE) and the Completed Richardson Extrapolation (CRE) with polynomial interpolation, to improve the accuracy of numerical solutions in Computational Fluid Dynamics (CFD) problems. The study focuses on reducing the field discretization error through the coupling of extrapolation techniques with SubGrid strategies, an aspect rarely explored in the literature. The proposed method, referred to as Richardson Extrapolation with SubGrid (RES), is evaluated and compared with the CRE-I, FRE, and RRES approaches using the Finite Difference Method (FDM) with the second-order central difference scheme (CDS-2). The 2D Poisson, 1D and 2D Burgers, and 2D Navier–Stokes equations are solved on uniform and non-uniform grids, with known analytical solutions used to assess the discretization error. The results show that RE and RRE with SubGrid effectively reduce the discretization error, allowing for accuracy orders of 12 and 34. The RES method exhibits superior performance due to the local transfer of extrapolated information between coincident grid points, which suppresses truncation errors before they propagate. These methods are robust, simple to implement, and constitute efficient post-processing tools for improving numerical accuracy in CFD simulations.</p>