FEM (Finite Element Method) based approximation model is proposed in this paper. Our goal is to solve a TV (Total Variation) denoising optimization problem using finite element method with triangular grid as a computational domain and also to study the local choice of smoothness parameters for the given problem. We provide some confidence measures in the form of average absolute error and average absolute square error corresponding to the different choices of locally selected regularization weights; moreover we show that how the regularization parameters play a crucial part in the reduction of error in the approximations and the diffusion enhancement specifically for this TV model