$H^1$-Galerkin Mixed Finite Element Method For The Sobolev Equation
Sobolev 方程的$H^1$-Galerkin混合有限元方法

In this paper, an $H^1$-Galerkin mixed finite element method is proposed to simulate the Sobolev equation. The problem is considered in $n$-dimentional($n\leq 3$) space, respectively. The unique existence of the semi-discrete and a fully discrete $H^1$-Galerkin mixed finite element solutions is proved, and optimal error estimates are also established. In particular, our method can simultaneously approximate the scalar unknown and the vector flux effectively, without requiring the LBB consistency condition. Finally, numerical results are provided to illustrate the efficiency of our method.