带罚混合问题在Taylor—Hood元逼近下的快速迭代法

对带罚混合问题的变异Ｔａｙｌｏｒ－Ｈｏｏｄ元逼近给出了一种快速迭代过程，基本思想是把带罚混合问题（对称不定问题）转换成一个正定系统，并证明它具有与网格步和攻罚项参数无关的有界条件数，采用共轭斜量法迭代求解这个系统，而每步的共轭斜量法迭代需要计算一个（二维）向量形式的Ｐｏｉｓｓｏｎ方程，它由多重网格法来近似计算，此算法对其它的满足ｉｎｆ－ｓｕｐ条件的有限元适用。

Fast Iterative Procedure for Mixed Problems with Penalty by Taylor- Hood Element Approximation

in this paper a fast iterative procedure for mixed problems with penalty by Taylor-Hood element approximation is presented. The original indefinite problem can be transformed into an equation involving a symmetric,positive definite, continuous system. It is proved that the condition number of the equation is bounded independently of the meshsize and of the penalty parameter. We use a conjugate gradient method to solve the equation. Each evaluation of one (CG) iterative step requires the solution of two discrete Poisson equations. This is done approximately using a multigrid algorithm. The generalization of the algorithm to the other elements, which satisfy the inf- sup condition, is discussed.