Optimality of an adaptive finite element method for the p-Laplacian equation

We consider the most standard adaptive finite element method (AFEM) with polynomial degree one for the nonlinear Laplacian. The method selects elements for refinement with Dörfler marking exclusively according to the error indicators. It performs minimal refinement in that no interior node condition is needed. For the sum of quasinorm error and oscillation we prove an error reduction rate. In combination with almost minimal Dörfler marking this yields an optimal decay rate in terms of degrees of freedom. A number of experiments confirm the optimal decay rates of the AFEM.