中文摘要：

本文研究Sobolev方程的连续时空有限元方法．首先建立Sobolev方程的连续时空有限元格式，然后证明了解的存在唯一性和稳定性并给出连续时空有限元解各种范数下的误差估计．最后给出数值算例来验证理论分析的正确性，并进一步说明本文所建立的格式关于时间可以得到比传统有限元方法更高的精度．

英文摘要：

In this paper we study the continuous space-time finite element method for Sobolev equation, the continuous space-time formulation is given firstly. And then, we prove the ex- istence, the uniqueness, and the stability of the continuous space-time finite element solution and give the error estimates of various norms of the continuous space-time finite element solution. Finally, we provide a numerical example to verify that correctness of theoretical analysis and to illustrate that the scheme established in this paper can obtain higher accuracy with respect to time than classical FE methods.