主要考虑用Legendre tau方法求解二维Poisson方程的Dirichlet问题.通过选取带有广义Jacobi权的函数作为检验函数,得到Legendre tau方法对于二维Poisson方程Dirichlet问题的H1模的最优误差估计;然后,通过对偶技巧,得到L2模的最优误差估计;最后,通过数值算例，进一步比较说明理论分析的结果.

The two-dimensional Poisson equation with homogeneous Dirichlet boundary condition by the Legendre tau method is considered. The optimal rate of convergence in H1norm of Legendre tau method for the two-dimensional Poisson equation with homogeneous Dirichlet boundary condition is obtained by taking test functions with the generalized Jacobi weight. The optimal convergent rate in Lnorm is proved by the duality argument. Numerical examples are given to verify the analysis results.