Finite element approximation for some quasilinear elliptic problems

We consider the finite element approximation of the boundary value problem −∇ · (A(u)∇u) = ƒ in Ω, u = 0 on ∂Ω, where Ω is a two- or three-dimensional polyhedral domain and A(u) is a Lipschitz continuous function satisfying A(u)⩾δ>0. Under the assumption of the uniqueness of the weak solution, we can show the L∞ convergence of the approximate solution.