Eigenvalue inclusions via domain decomposition

We describe a method for the calculation of guaranteed bounds for the K low est eigenvalues of second-order problems with Neumann boundary conditions. Using P-2 approximations for the eigenfunctions and RT1 approximations for the gradients of the eigenfunctions in H (div, Omega), an error bound for t he eigenfunctions is established for weak approximations in H-1 (Omega). In addition, the rest of the spectrum will be bounded by a domain decompositi on method; the eigenvalue problem is decomposed step-by-step into simpler g eometrical situations, where sufficient information on the spectrum is avai lable.