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Improvements for some condition number estimates for preconditioned system in \(p\)-FEM. (English) Zbl 1174.65540

Summary: We consider domain decomposition preconditioners for a system of linear algebraic equations arising from the \(p\)-version of the finite element method (FEM). We analyse several multi-level preconditioners for the Dirichlet problems in the sub-domains in two and three dimensions. It is proved that the condition number of the preconditioned system is bounded by a constant independent of the polynomial degree. Relations between the \(p\)-version of the FEM and the \(h\)-version are helpful in the interpretations of the results.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
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References:

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