Abstract: A two-grid partition of unity method for second order elliptic problems is proposed and analyzed. The standard two-grid method is a local and parallel method usually leading to a discontinuous solution in the entire computational domain. Partition of unity method is employed to glue all the local solutions together to get the global continuous one, which is optimal in H¹-norm. Furthermore, it is shown that the L² error can be improved by using the coarse grid correction. Numerical experiments are reported to support the theoretical results.

Key words: second order elliptic problems, two-grid method, partition of unity