Eigenvalue inclusions via domain decomposition

We describe a method for the calculation of guaranteed bounds for the K lowest eigenvalues of second–order problems with Neumann boundary conditions. Using P2 approximations for the eigenfunctions and RT1 approximations for the gradients of the eigenfunctions in H(div, ω), an error bound for the eigenfunctions is established for weak approximations in H1(ω). In addition, the rest of the spectrum will be bounded by a domain decomposition method; the eigenvalue problem is decomposed step–by–step into simpler geometrical situations, where sufficient information on the spectrum is available.