Abstract
This paper presents a partition of unity parallel finite element algorithm. This algorithm localizes the global residual problem of two grid method into some parallel local sub-problems, and use a simple partition of unity to assemble all the local solutions together. An oversampling technique is used and analyzed to decrease the undesirable effect of the artificial homogeneous Dirichlet boudary condition of local sub-problems. The analysis shows the error of this algorithm decays exponentially with respect to the oversampling parameter. Specially, on a regular coarse triangulation τ H with mesh size H, an oversampling of diameter \(H \log (1/H)\) is sufficient to preserve the optimal convergence order. Numerical results verify the theoretical analysis.
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Communicated by: Jinchao Xu
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Zheng, H., Song, L., Hou, Y. et al. The partition of unity parallel finite element algorithm. Adv Comput Math 41, 937–951 (2015). https://doi.org/10.1007/s10444-014-9392-x
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DOI: https://doi.org/10.1007/s10444-014-9392-x