Adaptive metric-based multigrid for a Poisson problem with discontinuous coefficients

In order to solve the linear partial differential equation Au = f, we combine two methods: Full-Multigrid method and Hessian-based mesh adaptation. First, we define independently an Hessian-based mesh adaptation loop and a FMG algorithm where, at each phase, the equation is solved by a preconditioned GMRES with multigrid as preconditioner. Then we insert the adaptive loop between the FMG phases. We use this new algorithm and we compare its results with those obtained with non-adaptive FMG