中文摘要：

时空有限元法将时间和空间两个变量统一起来,从而实现时间和空间两个方向的高精度.利用连续时空有限元法,对半线性奇异抛物方程进行了研究,给出有限元解的存在性证明和理论误差估计.

英文摘要：

In this paper a new variational method for approximating the semilinear singular parabolic equation is given by using continuous finite elements to discretize in space and time simultaneously.Higher accuracy is achieved in the two directions of space and time.The proof of existence of the finite element solution and their theoretical error estimates are presented.