摘要
给出了在一些Shiskin型网格 [2 1,2 3,19,18]上 ,利用一个任意次的混合有限元方法在L2 一模下得到奇异摄动问题解的最优一致收敛阶的一个统一方法 .通过研究一个四阶问题 ,定常和不定常问题 ,我们显示了这个方法的一般性 .结果显示非传统Shiskin型网格上的误差估计比传统Shiskin型网格上的误差估计更容易得到 .但两种网格给出的误差估计是相容的 ,它们证明了Roos的猜想 [2 1]是合理的 .
In this paper,a unified approach for obtaining optimal uniform convergence rates in the L 2-norm is presented for solving singularly perturbed problems by using an arbitrary order mixed finite element method on some Shishkin type meshes[21,23,19,18]. The generality of our techniques is showed by investigations of a fourth-order problem, steady and non-steady semilinear problems. The results show that the error estimates on the non-traditional Shishkin type mesh are much easier to prove than on the tradition Shishkin type mesh. However,both meshes give comparable error estimates,which justifies the conjecture of Roos.
出处
《数学研究》
CSCD
2001年第3期213-219,共7页
Journal of Mathematical Study
