Finite element approximation for some quasilinear elliptic problems

We consider the finite element approximation of the boundary value problem - del . (A(u)del u) = f in Omega, u=0 on partial derivative Omega, where Omega is a two- or three-dimensional polyhedral domain and A(u) is a Lipschitz continuous function satisfying A(u) greater than or equal to delta > 0. Under the assumption of the uniqueness of the weak solution, we can show the L-infinity convergence of the approximate solution. (C) 1998 Elsevier Science B.V. All rights reserved.