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We propose a novel universal construction of two-level overlapping Schwarz preconditioners for 2mth-order elliptic boundary value problems, where m is a positive integer. The word "universal" here signifies that the coarse space construction can be applied to any finite element discretization for any m that satisfies some common assumptions. We present numerical results for conforming, nonconforming, and discontinuous Galerkin-type finite element discretizations for high-order problems to demonstrate the scalability of the proposed two-level overlapping Schwarz preconditioners.
Jong-Ho Park (Wed,) studied this question.