TWO SPLITTING LEAST-SQUARES MIXED ELEMENT METHODS FOR LINEAR SOBOLEV EQUATIONS
求解线性Sobolev方程的分裂型最小二乘混合元方法

In this paper, two splitting least-squares mixed element methods are proposed to simulate a class of linear Sobolev equations. The methods' advantage is that the coupled system can be split into two independent sub-systems. Theoerical analysis shows that the methods yield the approximate solutions for the primal unknown with optimal accuracy in $L^2(\Omega)$ norm and for the unknown flux introdued with sub-optimal accuracy in $H(\mbox{div};\Omega)$ norm, respectively. Finally, some numerical examples are provided to illustrate the efficiency of the methods.