中文摘要：

在这份报纸，一个本地 multilevel 产品算法和它的添加剂版本为从第二份订单的适应 nonconforming P1 有限元素近似产生的线性系统被考虑椭圆形的边界价值问题。抽象 Schwarz 理论被使用与在最好的网孔上在粗糙的网孔和全球节点上在本地节点上执行的 Jacobi 或 Gauss-Seidel smoothers 分析 multilevel 方法。本地 multilevel 方法是最佳的，这被显示出，即， multilevel 方法的集中率独立于网孔尺寸和网孔层次。数字实验被给证实理论结果。[从作者抽象]

英文摘要：

In this paper, a local multilevel product algorithm and its additive version are con- sidered for linear systems arising from adaptive nonconforming P1 finite element approx- imations of second order elliptic boundary value problems. The abstract Schwarz theory is applied to analyze the multilevel methods with Jaeobi or Gauss-Seidel smoothers per- formed on local nodes on coarse meshes and global nodes on the finest mesh. It is shown that the local multilevel methods are optimal, i.e., the convergence rate of the multilevel methods is independent of the mesh sizes and mesh levels. Numerical experiments are given to confirm the theoretical results.