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Titlebook: Domain Decomposition Methods in Science and Engineering XIX; Yunqing Huang,Ralf Kornhuber,Jinchao Xu Conference proceedings 2011 Springer-

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On Adaptive-Multilevel BDDCctly becomes a bottleneck. Since the coarse problem has the same structure as the original problem, it is straightforward to apply the method recursively to solve it only approximately. The two-level BDDC analysis has been extended into three-levels in a pioneering work in [14, 15], and into a gener
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A New a Posteriori Error Estimate for Adaptive Finite Element Methodsto refine or adjust the mesh such that the errors are “equally” distributed over the computational mesh, with the aim of achieving a better accurate solution using an optimal number of degrees of freedom. By using the information from the approximated solution and the known data, the a posteriori er
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Convergence Behaviour of Dirichlet–Neumann and Robin Methods for a Nonlinear Transmission Problemcross two subdomains. In one space dimension, we obtain convergence theorems by extending known results from the linear case. They hold both on the continuous and on the discrete level. From the proofs one can infer mesh-independence of the convergence rates for the Dirichlet–Neumann method, but not
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Optimal Interface Conditions for an Arbitrary Decomposition into Subdomainsrations when the subdomain decomposition has tree-like connectivity. However, it remains an open problem whether it is possible to construct a finitely terminating algorithm for arbitrary decompositions. In this article, we construct a Schwarz method that converges in exactly two steps for any decom
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Optimized Schwarz Methods for Domains with an Arbitrary Interfacemploy a first or higher order boundary condition along the artificial interface to accelerate its convergence. In the literature, analysis of optimized Schwarz methods rely on Fourier analysis and so the domains are restricted to be regular (rectangle or disk). By expressing the interface operator i
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