中文摘要：

本文对于Sobolev方程提出并分析了两种新型数值方法：最小二乘Galerkin有限元法．这种方法的优越性在于不需要验证LBB条件，可以更好的选择有限元空间．误差估计表明在L^2（Ω））^2×L^2（Q）范数意义下，这两种方法均具有最优收敛阶，并且关于时间分别具有一阶精确度和二阶精确度．

英文摘要：

Two least-squares Galerkin finite element schemes are formulated to solve the initial-boundary value problem of Sobolev equations. The advantage of this method is that it is not subject to the LBB condition. The convergence analysis shows that the methods yield the approximate solutions with optimal accuracy in L^2（Ω））^2×L^2（Q）. Moreover, the schemes yield the approximate solutions with first-order and second-order accuracy in time increment, respectively.