Convergent adaptive finite elements for the nonlinear Laplacian

The numerical solution of the homogeneous Dirichlet problem for the p-Laplacian is considered. We propose an adaptive algorithm with continuous piecewise affine finite elements and prove that the approximate solutions converge to the exact one. While the algorithm is a rather straight-forward generalization of those for the linear case p=2, the proof of its convergence is different. In particular, it does not rely on a strict error reduction.