The Spectrum Computing Method Of Two Classes Mixed Variational Problems

This paper studies the spectrum computing method of two classes mixed variational problems.Based on spectrum method,the paper present respectively the theory analysis of error estimates about the second order elliptic and Stokes problem.The numerical examples of second order elliptic problem and Stokes problem is given. This dissertation employ the Spectral Methods. Using Fourier series approximate the true solution.Since using the finite series of infinity smooth function approximatively replace true solution.The method can get a better error estimate. Compared with the finite element method,spectrum method don’t need to decompose the computation domain Ω.The accuracy of approximate solution depend on the number of terms of series expansion.