Efficient Spectral-Galerkin Method for eigenvalue problems

Abstract—we provide a priori error estimates for linear elliptic eigenvalue problems based on the spectral-Galerkin method, and also provide an efficient Galerkin method is proposed for solving this problems,with this scheme,the solution of an eigenvalue problem on a big spectral space is reduced to the solution of an eigenvalue problem on a small spectral space and and solution of a linear algebraic system on the big spectral space and the resulting solution still maintains an asymptotically optimal accury. Keywords-eigenvalue; iterated galerkin method; priori error estimates; legendre polynomia I