摘要
对Sobolev方程采用H1-Galerkin混合有限元方法进行数值模拟．给出了一维空间中该方法的半离散和全离散格式及其最优误差估计;并将该方法推广到二维和三维空间．与H1-Galerkin有限元方法相比,该方法不仅降低了对有限元空间的连续性要求;而且与传统的混合有限元方法具有相同的收敛阶,但其有限元空间的选取却不需要满足LBB相容条件．数值例子将进一步说明该方法的可行性与有效性．
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≤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.
出处
《系统科学与数学》
CSCD
北大核心
2006年第3期301-314,共14页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(10271068)山东省自然科学基金(Y2002A01)资助课题.
