Mixed Finite Element And Spectral Method For Boundary Value Problems For Differential Equations

Mixed finite element method and Fourier spectral method for boundary value prob-lems are discussed in the text. A finite element method for solving the thin plate bending problem is proposed.The anisotropic characteristics of Hermite element interpolation can effectively be verified by constructing the standard node basic functions of cubic Her-mite rectangular element and then the error estimates of the fourth order problem's discrete scheme under the condition of regular subdivision and anisotropic subdivision are given. A mixed finite element method is presented and used to analyze the Bi-wave equation by employing the bilinear element. The existence and uniqueness of solution under the mixed variation formulation and discrete version are proved. Combined with the integral identities, error estimation can be improved the first convergence order. A Fourier spectral method for solving the variable coefficient elliptic problem is given. The existence and uniqueness of solution under the Fourier spectral formulation are certified and a half order of convergence is proposed.