Kacanov iterations for the p-Laplacian and minimal residual methods in W^{-1,p}

The first part of this talk introduces an iterative scheme for the computation of the discrete minimizer to the p-Laplace problem. The iterative scheme is easy to implement since each iterate results only from the solve of a weighted, linear Poisson problem. It neither requires an additional line search nor involves unknown constants for the step length. The scheme converges globally and its rate of convergence is independent of the underlying mesh. In the second part of the talk we adjust this ansatz to compute the minimizer of a minimal residual method in W^{-1,p}. The scheme remedies instabilities of finite element methods for problems like convection-dominated diffusion.