Finite element analysis for a nonlinear diffusion model in image processing

The optimal error estimate O(h^k+1) for a popular nonlinear diffusion model widely used in image processing is proved for the standard k^th-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].