Mathematics

We show that the h-adaptive mixed finite element method for the discretization of the eigenvalues of Laplace operator produces optimal convergence rates in terms of nonlinear approximation classes. The results are valid for the typical mixed spaces of Raviart-Thomas or Brezzi-Douglas-Marini type with arbitrary fixed polynomial degree in two and three dimensions. Our theory is cluster robust, in the sense that it allows for the simultaneous optimal approximation of the eigenvalues belonging to the same cluster. This is a joint work with D. Gallistl, F. Gardini, and L. Gastaldi.