ON A VARIATIONAL APPROXIMATION METHOD FOR A CLASS OF ELLIPTIC EIGENVALUE PROBLEMS IN COMPOSITE STRUCTURES

We consider a second-order elliptic eigenvalue problem on a convex pol ygonal domain, divided in M nonoverlapping subdomains. The conormal de rivative of the unknown function is continuous on the interfaces, whil e the function itself is discontinuous. We present a general finite el ement method to obtain a numerical solution of the eigenvalue problem, starting from a nonstandard formally equivalent variational formulati on in an abstract setting in product Hilbert spaces. We use standard L agrange finite element spaces on the subdomains. Moreover, the bilinea r forms are approximated by suitable numerical quadrature formulas. We obtain error estimates for both the eigenfunctions and the eigenvalue s, allowing for the case of multiple exact eigenvalues, by a pure vari ational method.