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Preconditioners based on various multilevel extensions of two-level finite element methods (FEM) lead to iterative methods which often have an optimal order computational complexity with respect to the number of degrees of freedom of the system. Such methods were first presented in [6, 7], and are based on (recursive) two-level splittings of the finite(More)
A. We construct optimal order multilevel preconditioners for interior-penalty dis-continuous Galerkin (DG) finite element discretizations of three-dimensional (3D) anisotropic elliptic boundary-value problems. In this paper we extend the analysis of our approach, introduced earlier for 2D problems [20], to cover 3D problems. A specific assembling(More)
Additive Schur complement approximation and application to multilevel preconditioning Powered by TCPDF (www.tcpdf.org) Abstract. In the present paper we introduce an algorithm for Additive Schur Complement Approximation (ASCA). This approximation technique can be applied in various iterative methods for solving systems of linear algebraic equations arising(More)
We derive a three-term recurrence relation for computing the polynomial of best approximation in the uniform norm to x −1 on a finite interval with positive endpoints. As application, we consider two-level methods for scalar elliptic partial differential equation (PDE), where the relaxation on the fine grid uses the aforementioned polynomial of best(More)