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An Expandable Local and Parallel Two-Grid Finite Element Scheme
An expandable local and parallel two-grid finite element scheme based on
superposition principle for elliptic problems is proposed and analyzed in this
paper by taking example of Poisson equation. Compared with the usual local and
parallel finite element schemes, the scheme proposed in this paper can be
easily implemented in a large parallel computer system that has a lot of CPUs.
Convergence results base on and a priori error estimation of the
scheme are obtained, which show that the scheme can reach the optimal
convergence orders within or two-grid iterations if the
coarse mesh size and the fine mesh size are properly configured in 2-D
or 3-D case, respectively. Some numerical results are presented at the end of
the paper to support our analysis