Upper and lower bounds for eigenvalues by finite differences
James R. Kuttler · Pacific Journal of Mathematics · 1970
Upper and lower bounds for the eigenvalues of elliptic partial differential equations associated with fixed membranes and clamped plates are given in terms of corresponding eigenvalues of their finite difference analogues.The upper bounds are found by interpolating piecewise polynomials through the solutions to the difference equations and substituting into the variational principle associated with the differential equations.The lower bounds are found by averaging the solutions to the differential equations and substituting into the discrete variational principle.