Joint work with Samuel Dubuis and Paride Passelli

Anisotropic, adaptive finite elements, that is finite elements with large aspect ratio, have been successfully used for various engineering applications, for instance aluminum electrolysis. The error estimator corresponding to space discretisation with continuous, piecewise linear finite elements will be presented for a diffusion problem. Numerical experiments on anisotropic, adapted meshes indicate that the effectivity index is close to a constant, even when the diffusion coefficient has strong variations. The error estimator corresponding to time discretisation, an order two BDF scheme, will be presented for the unsteady, incompressible Navier-Stokes equations. Again, numerical results for adapted meshes and time steps indicate that the effectivity index remains close to a constant.