A p-Laplacian like problem is considered. Using the anisotropic setting proposed by (Formaggia and Perotto, 2001, 2003), the error in a quasi-norm is bounded above by a residual-based error indicator. Following (Dubuis, Passelli and Picasso, 2022), an anisotropic adaptive strategy is presented. Numerical results show the sharpness of the error indicator on meshes with possible large aspect ratio and the efficiency of the adaptive algorithm. Finally, an application to Aluminium Electrolysis is presented. In particular, we focus on the incompressible Navier-Stokes equations with Smagorinsky viscosity introduced in (Rochat, 2016). The strategy developed for the p-Laplacian like problem is applied. Numerical results show that, for a given accuracy, the computational time is reduced by a factor 5 and the number of vertices by a factor 10, when comparing with non-adapted meshes.