Abstract
By combining the two-grid discretization with the partition of unity method, a parallel iterative finite element method for the linear elliptic equations is proposed and investigated. Since the construction of the partition of unity is based on the coarse mesh triangulation, the computational domain of each subproblem can be divided automatically and the number of subproblems can be arbitrarily huge as the coarse mesh parameter H tends to zero. That means our method can be easily implemented in high performance supercomputers or cluster of workstations. Theoretical results based on a priori error estimation of the scheme are obtained, which indicate that our method can reach the optimal convergence orders within a few two-grid iterations. Numerical results are reported to assess the theoretical results.
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