Finite element analysis for a nonlinear diffusion model in image processing Original Research Article

The optimal error estimate O(hk+1) for a popular nonlinear diffusion model widely used in image processing is proved for the standard kth-order (k ≥ 1) conforming tensor-product finite elements in the L2-norm. The optimal L2-estimate is obtained by the integral identity technique [1–3] without using the classic Nitsche duality argument [4].