Two-grid partition of unity method for second order elliptic problems

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.